Models for infant growth have usually been based on parametric forms, commonly an exponential or similar model, which have been shown to fit poorly especially during the first year of life. An alternative approach is to use a non-parametric model, based on a shape invariant model (SIM), where a single function is transformed by shifting and scaling to fit each subject. In the model a regression spline is used as the function, with log transformation of the data and a simplification of the SIM, obtained from the relationship with the exponential model. All subjects are fitted as a nonlinear mixed effects model, allowing the variation in the parameters between subjects to be determined. Methods for the inclusion of covariates in growth models based on SIM are developed, with parameters for time independent covariates included in the model by varying either the shape, the size parameter or the growth parameter and time-dependent co-variates included by transforming the time axis, to either increase or decrease the growth rate dependent on the co-variate, similar to methods used for accelerated failure-time models. The model is used to fit weight data for 602 infants, measured from 0 to 2 years as part of the Childhood Asthma Prevention Study (CAPS) trial, and to determine the effect of breastfeeding on infant weight.