A theory is presented for the fluid mechanical aspects of the impact of liquid drops, with rounded fronts, with a rigid surface. It is shown that for small collision Mach number (which corresponds to collisions under 300 m/s for water drops) there is a time period from a fraction of a microsecond after impact to several microseconds where an asymptotic expansion for small Mach number yields both complete and simple results. Explicit equations for the pressure at the interface are derived for both the two and three dimensional circular and spherical drop. Results are compared with other work. The asymptotic expansion procedure is interpreted in physical terms and suggestions for extensions of the present work are discussed