Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic samples of dimolybdenum carbide (alpha- Mo2C) as functions of temperature in the range 130 - 295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The temperature dependences of the shear elastic stiffness (mu) and Young's modulus ( E) show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. The longitudinal elastic stiffness ( CL) increases with decreasing temperature and shows a knee at about 200 K; the decrease in slope below the knee indicates longitudinal acoustic-mode softening. The adiabatic bulk modulus (B-S) is also affected by the mode softening below 200 K. The values obtained for the acoustic Debye temperature (Theta(D)) for ceramic alpha-Mo2C agree well with the thermal Debye temperature determined previously from heat capacity measurements. The velocities of both the longitudinal and shear ultrasonic waves in ceramic alpha-Mo2C increase approximately linearly with pressure: both the long-wavelength longitudinal and shear acoustic modes stiffen under pressure. The values determined at room temperature for the hydrostatic-pressure derivative (partial derivativemu/partial derivativeP)(P=0) of the shear stiffness is similar to those found for ceramic TiC and TaC; while (partial derivativeC(L)/partial derivativeP)(P=0) and (partial derivativeB(S)/partial derivativeP)(P=0) have large values, possibly due to the defect microstructure of ceramic alpha- Mo2C. (C) 2004 Kluwer Academic Publishers.