Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of titanium diboride (TiB2) ceramic samples as functions of temperature in the range 130-295 K and hydrostatic pressure up to 0.2 GPa at room temperature. TiB2 is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (C-L), shear stiffness (mu), adiabatic bulk modulus (B-S), Young's modulus (E) and Poisson's ratio (sigma) are 612 GPa, 252 GPa, 276 GPa, 579 GPa and 0.151, respectively. The adiabatic bulk modulus B-S is in good agreement with the results of recent theoretical calculations. All elastic moduli increase with decreasing temperature and do not show any pronounced unusual effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Gruneisen parameters. The values determined at 295 K for the hydrostatic-pressure derivatives (partial derivativeC(L)/partial derivativeP)(P=0), (partial derivative mu/partial derivativeP)(P=0) and (partial derivativeB(S)/partial derivativeP)(P=0) are 7.29 +/- 0.1, 2.53 +/- 0.1 and 3.91 +/- 0.1, respectively. The hydrostatic-pressure derivative (partial derivativeB(S)/partial derivativeP)(P)=0 of the bulk modulus of TiB2 ceramic is found to be larger than that estimated previously from uniaxial shock-wave loading experiments. The longitudinal (gamma (L)), shear (gamma (S)), and mean (gamma (el)) acoustic-mode Gruneisen parameters of TiB2 are positive: the zone-centre acoustic phonons stiffen under pressure in the usual way. Since the acoustic Debye temperature Theta (D) (=1190 K) is very high, the shear modes provide a substantial contribution to the acoustic phonon population at room temperature. Knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic TiB2. (C) Kluwer Academic Publishers.