Consider the solution of the capillary surface equation near a corner of the base domain. It is shown that there exists an asymptotic expansion of the height rise of the surface in a wedge when a+γ < π/2, where 2a is the corner angle and 0 < γ < π/2 the contact angle between the surface and the container wall. The asymptotic does not depend on the particular solution considered. In particular, the leading singularity which was discovered by Concus and Finn is equal to the solution up to O(r 3 ).