Farm-level data for the 1988/89 agricultural year from a sample survey of wheat farmers in Eastern Free State, are analysed in this paper. Stochastic frontier production functions are estimated, in which the technical inefficiency effects are modelled in terms of the size of the farming operation and other explanatory variables. The technical inefficiency effects for the farmers involved are significant and the null hypothesis that the explanatory variables in the model for the inefficiency effects have zero coefficients is rejected. The technical inefficiency effects are negatively and significantly related to the size of the farms. Elasticities of mean outputs with respect to the different inputs, together with the technical efficiencies of the wheat farmers, are estimated for both the translog and the Cobb-Douglas stochastic frontier production functions. However, the Cobb-Douglas function is not an adequate representation of the data, given the specifications of the translog stochastic frontier production function.