Felbinac, an active pharmaceutical ingredient (API) used clinically for the treatment of osteoarthritis, has poor solubility. Felbinac cataplasm product design was investigated using rheological and mechanical analyses. Experiments using a response surface methodology based on Box–Behnken design (BBD) incorporated three independent variables: the proportions of partially neutralized polyacrylate (NP800), dihydroxyaluminum aminoacetate (DAAA), and felbinac. Statistically significant quadratic models obtained using BBD demonstrated optimal NP-800, DAAA, and felbinac cataplasm proportions of 4.78–5.75%, 0.30–0.59%, and 0.70–0.90%, respectively. Felbinac cataplasms exhibited “gel-like” mechanical property with predominantly elastic behavior. Rheological studies correlated increasing NP-800 and DAAA concentrations with increased complex modulus (G*) values that were inversely related to peeling strength. Frequency sweep and creep tests revealed decreasing tan θ values with increasing NP-800 and DAAA concentrations. G’ and G” values were higher for higher NP-800 and DAAA levels, although G” values decreased with increasing DAAA concentration. Response surface methodology was applied to develop mathematical models. Variance analysis showed that the quadratic model effectively predicted felbinac and matrix material interactions, with two verification samples upholding model predictions. Relative errors between predicted and measured G* values were 3.28% and 1.10% and for peeling strength were 1.24% and 5.59%, respectively. In conclusion, rheological and mechanical analyses of felbinac cataplasms using BBD permits optimization of cataplasms as topical drug delivery vehicles.