The goal of the present study was to evaluate different mathematical models to describe the growth profiles of growing male kids. The kids used in the present study came from two experimental sets: one set of Alpine wethers (castrated at 15 days of age) and another set of Saanen kids. The variables measured in the first set were live weight (W), empty body weight (EBW), carcass weight, organs, empty gastrointestinal tract (GIT), skin, abdominal fat, trimmed cuts, blood, fresh GIT contents, and ruminoreticular fresh, dry matter, neutral detergent fiber, and lignin content at birth and at 15, 90, 135, 210, 270, and 365 days of age. The second set provided W and EBW of Saanen kids measured at 7, 37, 67, 142, and 195 days of age. The models tested were the monomolecular or Brody equation; the Gompertz, Richards, and generalized Michaelis-Menten models of sigmoid growth; and combinations of monomolecular and sigmoid models, forming biphasic models. In addition, four types of variance functions (covariance) were tested, namely, homogeneous, exponential, asymptotic, and power of the mean scaling function for each model. The model selection was based on the Akaike information criterion and its derived likelihood measures. The sigmoid simple models better described the time profiles, and the Gompertz model associated with homogeneous and scaled variances was the best choice for 57.1% of the growth profiles, most likely because of the ill-defined asymptotic phase; the biphasic models presented a lower likelihood probability of support. Nevertheless, the Brody-Gompertz and Brody-exponential growth biphasic models presented reasonable fits to certain variables, such as W, EBW, and carcass from both datasets. Therefore, despite the greater likelihood of the traditional growth functions, the biphasic models are promising for the description of the inflection points observed during the suckling-weaning and post-weaning phases of the goat kids’ growth profiles.