The purpose of this study is to develop methods of numerical optimization and sensitivity analysis of pultrusion process parameters. With this object in mind, a mathematical model of material behavior is implemented within ABAQUS environment, accounting for the dependence of matrix thermomechanical characteristics (elasticity moduli, CTE's, heat capacity and heat conductivity) on the temperature and the degree of polymerization. Modeling methods developed allow a researcher to predict of temperature, degree of curing and stress-strain distributions in a part during pultrusion process. For numerical optimization and sensitivity analysis of process parameters, a special simulation scheme was developed in pSeven software suite. pSeven is a platform for automation of engineering simulation and analysis tasks, multidisciplinary optimization and data mining. As an example, the process of pultrusion of GFRP (glass fiber reinforced plastic) rod with diameter of 80 mm is presented. The optimization parameters are the initial temperature of resin, temperatures in the 1-st and the 2-nd die zones, and pulling speed. To find optimum manufacturing parameters following constraints are considered: transverse stresses in the pultruded rod, maximum temperature of material, maximum temperature and degree of cure at the end (cut-off) section of the profile. As a result of optimization, guidelines on manufacturing process conditions have been developed allowing a pulling speed increase of 24 % to be achieved satisfying all constraints.