This paper explores a method to reduce the computational cost of stochastic finite element codes. The method, known as Gaussian process emulation, consists of building a statistical approximation to the output of such codes based on few training runs. The incorporation of emulation is explored for two aspects of the stochastic finite element problem. First, it is applied to approximating realizations of random fields discretized via the Karhunen-Loève expansion. Numerical results of emulating realizations of Gaussian and lognormal homogeneous two-dimensional random fields are presented. Second, it is coupled with the polynomial chaos expansion and the partitioned Cholesky decomposition in order to compute the response of the typical sparse linear system that arises due to the discretization of the partial differential equations that govern the response of a stochastic finite element problem. The advantages and challenges of adopting the proposed coupling are discussed. Copyright © 2011 John Wiley & Sons, Ltd.