This paper considers the shape invariant modelling approach in semiparametric regression estimation. Nonparametric regression functions of similar shape are linked by parametric transformations with unknown parameters. A computationally convenient estimation procedure is suggested. Finite sample performance of this estimator is investigated by simulations. Consistency of the parameter estimates is shown. An application to consumer data illustrates the importance of this method for applied statistics. Estimation results indicate that the imposed shape invariance restrictions have empirical evidence in the semiparametric modelling of consumer demand.