In this paper, we solve the kinetic problem of intense evaporation of molecular gas from a spherical particle into vacuum. We explicitly find the hydrodynamic boundary conditions for intense evaporation of diatomic and triatomic gases and demonstrate their strong dependence on the Knudsen number in the range 0 < Kn ≤ 0.1 (Kn = λ/r0, λ is the mean free path of molecules near the evaporating surface and r0 is the particle radius). This problem was not discussed in earlier papers [1–3]. We show that internal degrees of freedom lead to an appreciable decrease in the temperature jump and only slightly affect the gas concentration at the boundary of the Knudsen layer.