A Coriolis flowmeter: a flow tube for receiving a material flow; a balance bar coupled to said flow tube; a driver that vibrates said flow tube and said balance bar in a drive plane in phase opposition to each other; said vibrations in said drive plane and said material flow are jointly effective for inducing Coriolis deflections of said flow tube; pick off means (LS, RS) coupled to said flow tube that detect said Coriolis deflections; said pick off means generate signals representing information pertaining to said material flow in response to said detection of said Coriolis deflections; meter electronics that receive said signals from said pick off means and generates output information pertaining to said material flow; said Coriolis flowmeter is subject in operation to the presence of unwanted lateral vibrations of said flow tube in a plane substantially perpendicular to said drive plane; said lateral vibrations generate unwanted signals in said pick off means; said unwanted signals make difficult the processing of said pick off signals representing said Coriolis deflections when the frequency separation between said drive frequency and said lateral vibrations is less than a desired amount; Characterized by: lateral mode stabilizer means coupled to said flow tube and said balance bar, wherein said lateral mode stabilizer means includes: a first lateral mode stabilizer that couples a first end of said balance bar to a first wall portion of said flow tube; a second lateral mode stabilizer that couples a second end of said balance bar to a second wall portion of said flow tube; a ring element on each lateral mode stabilizer having a circular opening for receiving said flow tube; a first and a second lateral extension on said lateral mode stabilizer extending axially inward from said ring element towards a longitudinal center of said flow tube along the lateral sides of said flow tube; said lateral mode stabilizer means alters the frequency of said lateral vibrations to a greater extent than said drive vibrations and thereby increases the frequency separation between said drive frequency vibrations and the frequency of said lateral vibrations so that said separation is greater than said desired amount in order to facilitate the processing of said Coriolis signals by said meter electronics. a flow tube for receiving a material flow; a balance bar coupled to said flow tube; a driver that vibrates said flow tube and said balance bar in a drive plane in phase opposition to each other; said vibrations in said drive plane and said material flow are jointly effective for inducing Coriolis deflections of said flow tube; pick off means (LS, RS) coupled to said flow tube that detect said Coriolis deflections; said pick off means generate signals representing information pertaining to said material flow in response to said detection of said Coriolis deflections; meter electronics that receive said signals from said pick off means and generates output information pertaining to said material flow; said Coriolis flowmeter is subject in operation to the presence of unwanted lateral vibrations of said flow tube in a plane substantially perpendicular to said drive plane; said lateral vibrations generate unwanted signals in said pick off means; said unwanted signals make difficult the processing of said pick off signals representing said Coriolis deflections when the frequency separation between said drive frequency and said lateral vibrations is less than a desired amount; Characterized by: lateral mode stabilizer means coupled to said flow tube and said balance bar, wherein said lateral mode stabilizer means includes: a first lateral mode stabilizer that couples a first end of said balance bar to a first wall portion of said flow tube; a second lateral mode stabilizer that couples a second end of said balance bar to a second wall portion of said flow tube; a ring element on each lateral mode stabilizer having a circular opening for receiving said flow tube; a first and a second lateral extension on said lateral mode stabilizer extending axially inward from said ring element towards a longitudinal center of said flow tube along the lateral sides of said flow tube; said lateral mode stabilizer means alters the frequency of said lateral vibrations to a greater extent than said drive vibrations and thereby increases the frequency separation between said drive frequency vibrations and the frequency of said lateral vibrations so that said separation is greater than said desired amount in order to facilitate the processing of said Coriolis signals by said meter electronics. a first lateral mode stabilizer that couples a first end of said balance bar to a first wall portion of said flow tube; a second lateral mode stabilizer that couples a second end of said balance bar to a second wall portion of said flow tube; a ring element on each lateral mode stabilizer having a circular opening for receiving said flow tube; a first and a second lateral extension on said lateral mode stabilizer extending axially inward from said ring element towards a longitudinal center of said flow tube along the lateral sides of said flow tube; said lateral mode stabilizer means alters the frequency of said lateral vibrations to a greater extent than said drive vibrations and thereby increases the frequency separation between said drive frequency vibrations and the frequency of said lateral vibrations so that said separation is greater than said desired amount in order to facilitate the processing of said Coriolis signals by said meter electronics.