In this study, a model based on a modification of the Gompertz equation was used to estimate the maximum percentage of egg production and digestible requirements of lysine (Lys), methionine + cystine (Met + Cys) and threonine (Thr) of H&N brown laying hens during 16 weeks of production. The productive performance model was adjusted to field data of 23 treatments, which were defined from a composite central design that combines five levels of Lys, Met + Cys, and Thr ranged from 0.636% up to 1.000%; 0.579% up to 0.910%; 0.483% up to 0.760%, respectively. The proposed model showed to be adequate to evaluate the efficiency in the use of digestible amino acids for egg production and can be a useful tool to diagnose the effectiveness of the nutritional requirements in each of the production phases.