  We present a new method to compute quantum energies in presence of a
background field. The method is based on the string-inspired worldline approach
to quantum field theory and its numerical realization with Monte-Carlo
techniques. Our procedure is applied to the study of the Casimir force between
rigid bodies induced by a fluctuating real scalar field. We test our method
with the classic parallel-plate configuration and study curvature effects
quantitatively for the sphere-plate configuration. The numerical estimates are
compared with the ``proximity force approximation''. Sizable curvature effects
are found for a distance-to-curvature-radius ratio of a/R>0.02.
