The paper presents an original method concerning vibration suppression problem during milling of large-size and geometrically complicated workpieces with the use of novel way of selecting the spindle speed. This consists in repetitive simulations of the cutting process for subsequent values of the spindle speed, until the best vibration state of the workpiece is reached. An appropriate method of obtaining a computational model, called a modal approach, consists in identifying the parameters of the workpiece model created using the Finite Element Method (FEM). Thanks to the results of the identification of the modal subsystem obtained by the Experimental Modal Analysis (EMA) method, it can be stated that the parameters obtained from the experiment and delivered from the computational model have been correctly determined and constitute reliable process data for the simulation tests. The Root Mean Square (RMS) values of time domain displacements are evaluated. The efficiency of the proposed approach is evidenced by chosen technique of mechatronic design, called Experiment Aided Virtual Prototyping (EAVP). The proposed method is verified on the basis of the results of the experimental research of the relevant milling process.