The symplectic packing problem is the study of obstructions beyond volume for the existence of a symplectic embedding of ball into a symplectic manifold M. This question has connections with algebraic geometry via the study of symplectic forms on the blow-up of M and it also arises in connection with estimates for pseudo-differential operators. For a Lagrangian submanifold L in M one can study the relative packing problem where one tries to symplectically embed a ball in M so that it intersects the Lagrangian exactly along the real part of the ball and this gives a quantitative symplectic measurement of the size of the Lagrangian. In this talk I will present a wrapped Floer cohomomology construction using geodesic flow on L to give obstructions to such relative embeddings. This is joint work in progress with Mark McLean.