Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic boron carbide (B4C) as functions of temperature in the range 160-295 K and hydrostatic pressure up to 0.2 GPa at room temperature. B4C is an elastically stiff but extremely 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 498 GPa, 193 GPa, 241 GPa, 457 GPa and 0.184, respectively. In general, the adiabatic bulk modulus B-S agrees well with both experimental and theoretical values determined previously and is approximately constant over the measured temperature range. Both E and mu increase with decreasing temperature and do not show any unusual effects. The values determined at 295 K for the hydrostatic-pressure derivatives (partial derivative C-L/partial derivativeP)(P=0), (partial derivativemu/partial derivativeP)(P=0) and (partial derivativeB(S)/partial derivativeP)(P=0) are 5.7+/- 0.3, 0.78+/-0.4 and 4.67+/-0.3, respectively. The hydrostatic-pressure derivative (partial derivativeB(S)/partial derivativeP)(P=0) of the bulk modulus is found to be comparable with that estimated previously from dynamic yield strength measurements. 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 Gru neisen parameters. The longitudinal (gamma(L)), shear (gamma(S)), and mean (gamma(el)) acoustic-mode Gruneisen parameters of B4C are positive: the zone-centre acoustic phonons stiffen under pressure in the usual way. Knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic B4C. Since the acoustic Debye temperature Theta(D) (=1480 K) is very high, the shear modes provide a substantial contribution to the acoustic phonon population at room temperature.