Two types of capillary–gravity interfacial solitary waves are computed numerically: ‘classical’ solitary waves which bifurcate from a uniform flow at a critical value of the velocity and solitary waves in the form of wave packets which bifurcate from a train of infinitesimal periodic waves with equal phase and group velocities. The effects of finite amplitude are shown to be quite different from the pure gravity case for the classical solitary waves. The solitary waves in the form of wave packets, which are known to exist for small density ratios, are shown to exist even for larger density ratios, but only at finite amplitude. The numerical code is based on an integro-differential formulation of the full Euler equations. The experimental results of Koop & Butler (1981), which have been compared earlier with results from model equations, are compared with the present numerical results.