  In this paper we show how the stochastic quantization method developed by
Parisi and Wu can be used to obtain Casimir forces. Both quantum and thermal
fluctuations are taken into account by a Langevin equation for the field. The
method allows the Casimir force to be obtained directly, derived from the
stress tensor instead of the free energy. It only requires the spectral
decomposition of the Laplacian operator in the given geometry. The formalism
provides also an expression for the fluctuations of the force. As an
application we compute the Casimir force on the plates of a finite piston of
arbitrary cross section. Fluctuations of the force are also directly obtained,
and it is shown that, in the piston case, the variance of the force is twice
the force squared.
