Among the sheet metal forming processes, hydrodynamics deep drawing and hydromechanical deep drawing process are two main types of the deep drawing process that can fabricate complicated parts. In the hydroforming process, the blank is formed to the desired shape by applying a considerably high hydraulicpressure. In this article, the selection of the process parameters will be investigated during the manufacturing of a pure copper sharp conical part by finite element analysis and experimental tests. Two finite element models aredeveloped for hydrodynamics deep drawing and hydromechanical deep drawing processes. After verification of the FE model by experimental results, the effect of process parameters includes the applied pressure, friction coefficient, die radius and blank holder force on thinning of the blank are investigated. The thinning ratio of blank is calculated in different zones of the conical part under different working conditions determined according to the Taguchi design of experiment methods. Signal to noise ratio analysis has been carried out and the influence of process parameters on the thinning ratio is determined at different zones of the conical part. The results show that the friction coefficient has an important role in the thinning of the conical nose while at the lateral surface of the cone, the die radius is the most effective parameter on the thinning ratio. The results showthat by implementing statistical tools (Taguchi method and signal to noise ratio analysis), it is possible to select the proper process parameters conditions and fabricate defect-free parts. In addition, a non-linear regression equation is developed for prediction of thinning ratio in the hydrodynamics deep drawing and hydromechanical deep drawing processes.