The first three essential amino acids (EAA) for broilers including methionine (Met), lysine (Lys) and threonine (Thr) may greatly influence the growth of chick muscles at early stages of life. In order to survey the potential effects of those EAA on growth muscles, a rotatable three-variable central composite design (CCD) was conducted to track the interrelationships of dietary digestible Met (dMet), Lys (dLys) and Thr (dThr) for optimization of processing yields in broiler chicks using response surface methodology. A total of 60 floor pens of six birds each were assigned to 15 dietary treatments based on CCD containing five levels of dMet (0.416% to 0.584% of diet), dLys (0.881% to 1.319% of diet) and dThr (0.532% to 0.868% of diet) from 3 to 16 days of age. Experimental treatments significantly affected breast mass (BM) and leg mass (LM) of the birds (P<0.05) in which the main effect of dLys on BM was threefold higher than the main effect of dThr, and interaction effect between dMet and dLys was observed on BM (P<0.05). However, in the case of LM, the main effect of dThr was higher than the main effects of dMet and dLys and highest interaction effect exist between dThr and dMet (P<0.05). The second-order models for BM and LM were fitted by least squares regression. Canonical analysis revealed that the stationary points for carcass components were saddle points, thus ridge analysis was performed for getting optimal values of each EAA. Ridge analyses of BM and LM models showed that the maximum BM point may be obtained with 0.58%, 1.05% and 0.76% of dMet, dLys and dThr, respectively, in diet, and maximum LM point may be achieved with 0.58%, 1.09% and 0.70% of dMet, dLys and dThr, respectively, in diet. The resultant ideal ratios of dMet and dThr to dLys were 55% and 72% for BM; 53% and 64% for LM. Moreover, sensitivity analysis showed that the most important amino acids in BM and LM models were Lys and Thr, respectively. In conclusion, providing these three amino acid for BM optimization may warrant LM optimization and higher ideal ratios of dMet and dThr for breast muscle may indicate the higher importance of these EAA in this muscle than those in thigh muscle.