The problem of normal impact of a rigid sphere onto a Maxwell viscoelastic solid half-space is considered. The first-order asymptotic solution is constructed in the framework of Hunter’s model of viscoelastic impact [Hunter, S. C., 1957. Energy absorbed by elastic waves during impact. Journal of the Mechanics and Physics of Solids, 5(3), 162–171.]. In particular, simple analytical approximations have been derived for the maximum contact force and the time to achieve it. A linear regression method is suggested for evaluating the instantaneous elastic modulus and the mean relaxation time from a set of experimental data collected for different impactors and impact velocities.