We develop a non-dynamic panel smooth transition regression model with fixed individual effects. The model is useful for describing heterogenous panels, with regression coefficients that vary across individuals and over time. Heterogeneity is allowed for by assuming that these coefficients are continuous functions of an observable variable through a bounded function of this variable and fluctuate between a limited number (often two) of extreme regimes. The model can be viewed as a generalization of the threshold panel model of Hansen (1999). We extend the modelling strategy for univariate smooth transition regression models to the panel context. This comprises of model specification based on homogeneity tests, parameter estimation, and diagnostic checking, including tests for parameter constancy and no remaining nonlinearity. The new model is applied to describe firms' investment decisions in the presence of capital market imperfections.