This paper compares the generality, accuracy and computational speed of alternative approaches to solving linear rational expectations models, including the procedures of Sims (Solving linear rational expectations models, 1996), Anderson and Moore (Unpublished manuscript, 1983), Binder and Pesaran (Multivariate rational expectations models and macroeconometric modelling: A review and some new results, 1994), King and Watson (International Economic review, 39, 1015–1026, 1998), Klein (Journal of Economic Dynamics and Control, 24, 1405–1423, 1999), and Uhlig (A toolkit for analyzing nonlinear dynamic stochastic models easily, 1999). While all six procedures yield equivalent results for models with a unique stationary solution, the algorithm of Anderson and Moore (Unpublished manuscript, 1983) is the fastest and provides the highest accuracy; furthermore, the speed advantage increases with the size of the model.