  On the basis of quasipotential method in quantum electrodynamics we calculate
nuclear finite size radiative corrections of order $\alpha(Z \alpha)^5$ to the
Lamb shift in muonic hydrogen and helium. To construct the interaction
potential of particles, which gives the necessary contributions to the energy
spectrum, we use the method of projection operators to states with a definite
spin. Separate analytic expressions for the contributions of the muon
self-energy, the muon vertex operator and the amplitude with spanning photon
are obtained. We present also numerical results for these contributions using
modern experimental data on the electromagnetic form factors of light nuclei.
