Abstract We apply Polynomial chaos expansion (PCE) to surrogate time-consuming repeated model evaluations for different parameter values. PCE represents a random variable, the quantity of interest (QoI), as a series expansion of other random variables, the inputs. Repeated evaluations become inexpensive by treating uncertain parameters of a model as inputs, and an element of a model’s solution, e.g., the policy function, second moments, or the posterior kernel as the QoI. We introduce the theory of PCE and apply it to the standard real business cycle model as an illustrative example. We analyze the convergence behavior of PCE for different QoIs and its efficiency when used for estimation. The results are promising both for local and global solution methods.