This study investigates the foreign trade elasticities of the oil, non-oil, and services sectors of the Azerbaijani economy, aiming to understand how consumers substitute between imported and domestic goods and how producers allocate output between domestic and foreign markets. CES-type Armington and Constant Elasticity of Transformation (CET) functions are estimated using the Marquardt nonlinear optimization method in Mathcad, providing a consistent framework for capturing substitution and transformation behaviors across sectors. The results reveal substantial intersectoral differences in both demand-side and supply-side elasticities, reflecting structural characteristics that shape the country’s trade patterns. Although the estimated elasticities are derived under the assumption of stable behavioral relationships over time, the analysis offers valuable implications for policy assessment. In particular, the elasticities can be directly used in the calibration of general equilibrium and trade models designed to evaluate alternative policy scenarios. The study provides original sector-specific empirical estimates for Azerbaijan, contributing to a better understanding of foreign trade responses and supporting model-based policy design.