Application of optimization techniques to the identification of inelastic material parameters has substantially increased in recent years. The complex stress–strain paths and high nonlinearity, typical of this class of problems, require the development of robust and efficient techniques for inverse problems able to account for an irregular topography of the fitness surface. Within this framework, this work investigates the application of the gradient-based Sequential Quadratic Programming method, of the Nelder–Mead downhill simplex algorithm, of Particle Swarm Optimization (PSO), and of a global–local PSO–Nelder–Mead hybrid scheme to the identification of inelastic parameters based on a deep drawing operation. The hybrid technique has shown to be the best strategy by combining the good PSO performance to approach the global minimum basin of attraction with the efficiency demonstrated by the Nelder–Mead algorithm to obtain the minimum itself.