The decomposition of antibiotics (cefaclor) by gamma irradiation in aqueous solutions was experimentally evaluated. To obtain a mutual interaction between two factors (antibiotics concentrations and radiation doses) and to optimize these factors during the process, experimental design and statistical analysis were employed. The decomposition capability of the gamma radiation was also mathematically described as a function of cefaclor concentration and gamma-ray dose using the statistical analysis. The results showed that the cefaclor concentration ($X_1$) in the response $Y_1$ (Reduction of cefaclor concentration) and gamma-ray dose ($X_2$) in the response $Y_2$ (Removal efficiency (%) of cefaclor concentration) exhibited a significantly positive effect, whereas gamma-ray dose ($X_2$) in the response $Y_1$ showed a significantly negative effect. The estimated ridge of maximum responses and optimal conditions for $Y_1$:($X_1$,$X_2$)=(25 mg/L, 350 Gy) and $Y_2$:($X_1$,$X_2$)=(21 mg/L, 565 Gy) using canonical analysis were 4.37 mg/L of reduction of cefaclor concentration and 98.35% of removal efficiency of cefaclor concentration, respectively. The measurement values agreed well with the predicted ones, thereby confirming the suitability of the model for $Y_1$ and $Y_2$ and the success of the experimental design in optimizing the conditions of the gamma irradiation process.