The thirteen adiabatic elastic stiffness moduli of triglycine sulphate (TGS) have been determined at room temperature from measurements of the ultrasound wave velocities. Results are used to describe the elastic behaviour of TGS. Accidental pure mode directions have been found at 9.4 ~ and 106.5 ~ A method has been developed for obtaining the hydrostatic pressure derivatives (aClj/~P) of the elastic constants of a monoclinic crystal from the hydrostatic pressure dependences of ultrasound wave velocities. This method has been applied to find the ~CIj/~P for TGS. There is no evidence for acoustic phonon mode softening under pressure.

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