The paper considers the creation and research of a virtual prototype of titanium blanks drilling using the Lagrange and Galerkin method. The developed finite-element models are designed to study the process of mechanical treatment and optimize technological cutting parameters. The paper presents the results of computational investigation of titanium blanks drilling using mathematical modeling programs, which allow complete simulating operating procedures in a computer (digital twin). As a program to simulate the process of removing the allowance from a titanium workpiece, the authors used a multipurpose software product of finite-element modeling and analysis of highly-linear dynamic processes using various Ls-DYNA time integration schemes. The application of the Galerkin method allows adequately describing the drilling process with the introduction of the ultrasonic field energy into a treatment zone, can significantly reduce the duration of experimental research and evaluates the influence of the cutting mode elements and the tool design parameters on the power and energy aspects of the formation of new machine parts surfaces. Both methods are applicable to create various processes of mechanical treatment, however, the Lagrange method is less sensitive to the ultrasonic field energy. The introduction of the ultrasonic field energy into the drilling zone of workpieces made of hard-processing titanium alloys can significantly reduce energy costs. As a result of the simulation, the authors obtained a calculation file containing the simulation process, the solution of which visually reflects the drilling process of a titanium workpiece in a real-life setting with the removal of chips. However, for complete verification of numerical study results, it is necessary to carry out an experimental check and make adjustments to the calculated data.