Corrections to vacuum forces resulting from small distortions of the geometry of a region

Perturbation theory is developed for calculating the first order corrections to eigenmodes of zero oscillations of electromagnetic field in a closed region arising due to small distortions of the geometry of this region. Expressions for the vacuum energy density and vacuum force between the boundaries of a parallelepiped with various kinds of roughness are obtained. Corrections to the Casimir forces between non-parallel and curved plates are also evaluated.