A computer-implemented method for evaluating a material on a remote side of a partition constituted by the wall of a casing that is installed in a borehole, thus separating a first domain inside the casing from a second domain outside the casing, the method comprising: activating at least one ultrasonic transmitter (T 1) disposed inside the casing to form ultrasonic waveforms that comprise propagated quasi leaky-Lamb waves constituting an extensional wave and a flexural wave having respective symmetrical and antisymmetric zero-order modes within the wall of the casing; and recording the ultrasonic waveforms by a plurality of ultrasonic receivers (R 1, R 2),,the at least one ultrasonic transmitter (T 1) and the plurality of ultrasonic receivers (R 1, R 2) being disposed in longitudinally spaced-apart relationship along a first side of the wall of the casing in the first domain; characterized by: processing the recorded ultrasonic waveforms to determine a measured phase velocity of the waves propagating through the second domain on a second side of the casing from a first receiver (R 1) to a second receiver (R 2) that is located more remote from the transmitter (T 1) than the first receiver (R 1) and whose separation from the first receiver (R 1) is known; computing an analytical phase velocity of the flexural wave propagating through the second domain outside the casing; and establishing that the second domain outside the casing between the wall of the casing and the borehole contains a solid if there is a deviation of the measured phase velocity from the analytical phase velocity in the frequency domain by an amount that is not accountable by noise alone. activating at least one ultrasonic transmitter (T 1) disposed inside the casing to form ultrasonic waveforms that comprise propagated quasi leaky-Lamb waves constituting an extensional wave and a flexural wave having respective symmetrical and antisymmetric zero-order modes within the wall of the casing; and recording the ultrasonic waveforms by a plurality of ultrasonic receivers (R 1, R 2),,the at least one ultrasonic transmitter (T 1) and the plurality of ultrasonic receivers (R 1, R 2) being disposed in longitudinally spaced-apart relationship along a first side of the wall of the casing in the first domain; characterized by: processing the recorded ultrasonic waveforms to determine a measured phase velocity of the waves propagating through the second domain on a second side of the casing from a first receiver (R 1) to a second receiver (R 2) that is located more remote from the transmitter (T 1) than the first receiver (R 1) and whose separation from the first receiver (R 1) is known; computing an analytical phase velocity of the flexural wave propagating through the second domain outside the casing; and establishing that the second domain outside the casing between the wall of the casing and the borehole contains a solid if there is a deviation of the measured phase velocity from the analytical phase velocity in the frequency domain by an amount that is not accountable by noise alone. processing the recorded ultrasonic waveforms to determine a measured phase velocity of the waves propagating through the second domain on a second side of the casing from a first receiver (R 1) to a second receiver (R 2) that is located more remote from the transmitter (T 1) than the first receiver (R 1) and whose separation from the first receiver (R 1) is known; computing an analytical phase velocity of the flexural wave propagating through the second domain outside the casing; and establishing that the second domain outside the casing between the wall of the casing and the borehole contains a solid if there is a deviation of the measured phase velocity from the analytical phase velocity in the frequency domain by an amount that is not accountable by noise alone.