We consider corrections to the Lamb shift of p-wave atomic states due to the finite nuclear size (FNS). In other words, these are radiative corrections to the atomic isotop shift related to FNS. It is shown that the structure of the corrections is qualitatively different from that for s-wave states. The perturbation theory expansion for the relative correction for a $p_{1/2}$-state starts from $alphaln(1/Zalpha)$-term, while for $s_{1/2}$-states it starts from $Zalpha^2$ term. Here $alpha$ is the fine structure constant and $Z$ is the nuclear charge. In the present work we calculate the $alpha$-terms for $2p$-states, the result for $2p_{1/2}$-state reads $(8alpha/9pi)[ln(1/(Zalpha)^2)+0.710]$. Even more interesting are $p_{3/2}$-states. In this case the ``correction is by several orders of magnitude larger than the ``leading FNS shift.
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