Single ellipsoidal particles have been simulated during collision with a semi-infinite plane wall, using a 'softsphere' technique modified for a non-sphere. These simulations have several complications compared to those for spheres, including greater interaction between normal, tangential and rotational velocities. The normal force is calculated assuming perfectly elastic behaviour; the Hertz formulation specifies the variation of normal stiffness with curvature of the body. It is shown that variations in normal stiffness will cause a torque during rolling. Equations are presented in detail for the calculation of the contact point's location and curvature, and for the time-stepping scheme used in the simulations. It is assumed that motion is in a plane of symmetry of the ellipsoid, with zero initial rotational velocity. The convergence of this scheme is tested, and characteristics of the collision are expressed in terms of dimensionless groups. The resulting rebound behaviour is also quite complicated: multiple collisions are common; the coefficient of restitution varies considerably with initial orientation and can be greater than unity; particles can acquire back-spin or topspin, and may rebound backwards. Mean values and standard deviations are reported for the rebound velocities from a full sample of initial orientations. The standard deviations are relatively insensitive to aspect ratios in the range 2 to 8. These results may be of use in 'hard-sphere' simulations of non-spherical particles colliding with walls.