This paper combines Feasible Sequential Quadratic Programming (FSQP) and elasto-plastic finite element method to perform the inverse estimation of the material constitutive constants and fiction coefficient in the nosing process. The aim is to improve the accuracy of constitutive constants and working parameters in the classical analysis based on the material flow homogeneity or trial and error. In the prediction of the friction coefficient at the interface between metal and tool surface, the simulated load, calculated from the optimal material constants, shows good coincidence with the experimental load when the optimal friction coefficient is reached. The investigation of these inverse models identify that the combination of FSQP and elasto-plastic finite element method can supply a useful optimal approach in the industrial application.