This chapter presents the results of experimental studies and numerical modeling of the effect of frictionFriction between a steel indenter and thin sheets of titanium alloys CP Ti and Ti-5Al-2.5Sn on the evolution of the stress-strain state and crack formation at punching rates from 0.5 to 1, 5, 10 m/s. The study was carried out for an indenter that had a hemispherical shape with a diameter of 20 mm. The tests were carried out on an Instron VHS 40/50-20 servo-hydraulic stand with constant loading rates using Gazpromneft Grease High-Speed IPF ER-3 lubricant between the indenter and titanium samples with and without a lubricant. The change in punching force over time was recorded during the loading process until the complete destruction of the sample. The formation of cracks during punching was studied by high-speed video recording using a Phantom V711 of the back surface of the plates during the punching process. The stress state in the plate near the center of the contact area between the samples and the indenter is close to the biaxial tensile stress state. It has been established that by decreasing the friction coefficient at the contact surface, the force corresponding to the initiation of cracks increases for all punching speeds in the studied range. The rising friction coefficient is caused by the increasing contact surface roughness of Ti-5Al-2.5 samples due to the formation of wear marks and local damages. It was found that at indenter speeds from 5 to 10 m/s, an increase in the friction coefficient leads to the initiation and development of radial cracks. The analysis of plastic deformation evolution and crack formation was carried out by numerical simulation using LS-DYNA in WB ANSYS 2019b.