  Let (M, {\pi} ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives
rise to an algebroid $AP \rightarrow P$, to which we associate certain
chomology groups which control formal deformations of {\pi} around P . Assuming
that these groups vanish, we prove that {\pi} is formally rigid around P , i.e.
any other Poisson structure on M , with the same first order jet along P as
{\pi} is formally Poisson diffeomorphic to {\pi} . When P is a symplectic leaf,
we find a list of criteria which imply that these cohomological obstructions
vanish. In particular we obtain a formal version of the normal form theorem for
Poisson manifolds around symplectic leaves.
