A multiscale expansion approach is applied to the solution of the free‐boundary Stokes’ problem describing flow in the vicinity of a moving contact line. A solution free of singularities is obtained for the case of a liquid advancing into an inviscid medium. The force singularity reported in earlier studies is relaxed as the dynamic contact angle approaches &pgr; in the immediate vicinity of the moving contact line. This solution formally breaks down at a nonvanishing viscosity ratio of the receding and advancing fluids, but it still holds approximately for the case of a volatile liquid advancing into gas when Stefan flow in the gas phase is taken into account.