<PAGE>   1
                                                                      Exhibit 24

                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


February 27, 1998                           /s/ CRAIG R. ANDERSSON
--------------------------------            --------------------------------
          (Date)                            Craig R. Andersson
<PAGE>   2


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


February 27, 1998                           /s/ NEIL A. ARMSTRONG
--------------------------------            --------------------------------
          (Date)                            Neil A. Armstrong
<PAGE>   3


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


March 3, 1998                               /s/ DANIEL I. BOOKER
--------------------------------            --------------------------------
          (Date)                            Daniel I. Booker
<PAGE>   4


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


March 2, 1998                               /s/ RONALD L. GALLATIN
--------------------------------            --------------------------------
          (Date)                            Ronald L. Gallatin
<PAGE>   5


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


March 2, 1998                               /s/ CHARLES C. GEDEON
--------------------------------            --------------------------------
          (Date)                            Charles C. Gedeon
<PAGE>   6


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


February 27, 1998                           /s/ ROBERT M. HERNANDEZ
--------------------------------            --------------------------------
          (Date)                            Robert M. Hernandez
<PAGE>   7


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


February 27, 1998                           /s/ DANA J. JOHNSON
--------------------------------            --------------------------------
          (Date)                            Dana J. Johnson
<PAGE>   8


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


February 26, 1998                           /s/ JOHN H. OLDE
--------------------------------            --------------------------------
          (Date)                            John H. Olde
<PAGE>   9


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


February 25, 1998                           /s/ TIMOTHY G. RUPERT
--------------------------------            --------------------------------
          (Date)                            Timothy G. Rupert
<PAGE>   10


                               POWER OF ATTORNEY


KNOWN ALL MEN BY THESE PRESENTS:


     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or John H. Odle, my true and lawful attorney-in-fact, to sign and execute
for me and on my behalf, the Annual Report on Form 10-K for the year 1997 for
RMI Titanium Company, and any and all amendments thereto to be filed with the
Securities and Exchange Commission pursuant to the Securities Exchange Act, as
amended, in such form as they or any one or more of them may approve, and to do
any and all other acts which said attorney-in-fact may deem necessary or
desirable to enable RMI Titanium Company to comply with said Act and the rules
and regulations thereunder.

     In WITNESS WHEREOF, I have hereunto set my hand and seal.


March 3, 1998                               /s/ WESLEY W. VON SCHACK
--------------------------------            --------------------------------
          (Date)                            Wesley W. von Schack