Until now, the problem of the effect of alloying elements on the development stage of atomic displacement cascades in vanadium-based alloys, which are considered as a promising group of radiation-resistant materials for thermonuclear energy, has not been investigated. In this paper, a molecular dynamic study of the atomic displacement cascade development in pure vanadium and V-Ti alloys with titanium concentrations of 4, 8, and 16 % is carried out for energies of a primary knocked-out atom of 5, 10, and 20 keV. The interactions between atoms in the V-Ti system are specified in the framework of a method developed earlier for modeling systems with metallic and covalent types of chemical bond. The interactions at small interatomic distances are taken into account for screened ions which allows one to correctly simulate atomic systems under high-energy conditions. The simulations were carried out at 700 K that corresponds to the lower limit of the operating temperature range of the alloys. The purpose of the work is to establish the features of the effect of titanium on the cascade characteristics and the possibility of reducing the radiation swelling by titanium doping. The main characteristics of cascades considered in this paper are the number of generated defects at different stages of a cascade and the structure of the radiation-damaged region. The distribution of surviving defects of vacancy and interstitial types is calculated in accordance with the concentration of titanium and energy of a primary knocked-out atom. It has been proved that titanium doping results in a decrease in the size of the vacancy clusters formed after cascades.