Population viability analysis is an important tool for conservation biologists, and matrix models that incorporate stochasticity are commonly used for this purpose. However, stochastic simulations may require assumptions about the distribution of matrix parameters, and modelers often select a statistical distribution that seems reasonable without sufficient data to test its fit. We used data from long-term (5–10 year) studies with 27 populations of five perennial plant species to compare seven methods of incorporating environmental stochasticity. We estimated stochastic population growth rate (a measure of viability) using a matrix-selection method, in which whole observed matrices were selected at random at each time step of the model. In addition, we drew matrix elements (transition probabilities) at random using various statistical distributions: beta, truncated-gamma, truncated-normal, triangular, uniform, or discontinuous/observed. Recruitment rates were held constant at their observed mean values. Two methods of constraining stage-specific survival to ≤100% were also compared. Different methods of incorporating stochasticity and constraining matrix column sums interacted in their effects and resulted in different estimates of stochastic growth rate (differing by up to 16%). Modelers should be aware that when constraining stage-specific survival to 100%, different methods may introduce different levels of bias in transition element means, and when this happens, different distributions for generating random transition elements may result in different viability estimates. There was no species effect on the results and the growth rates derived from all methods were highly correlated with one another. We conclude that the absolute value of population viability estimates is sensitive to model assumptions, but the relative ranking of populations (and management treatments) is robust. Furthermore, these results are applicable to a range of perennial plants and possibly other life histories.