Since it is the dominant paradigm of the business cycle and growth lit
eratures, the stochastic growth model has been used to test the perfor
mance of alternative numerical methods, In this paper I apply the fini
te element method to this model. I show that the method is easy to app
ly and that, for examples such as the stochastic growth model, it give
s accurate solutions within a second or two on a desktop computer. I a
lso show how inequality constraints can be handled by redefining the o
ptimization problem with penalty functions.