This work aims to determine the Kearns texture parameters and evaluate on their basis the elastic moduli, mechanical properties (ultimate tensile strength, conditional yield stress), as well as damageability parameters of the sheets commercial titanium (CT-grade 1: 0.04% Fe; 0.015% C; 0.05% N 0.05% c; 0.009% H) as delivered after rolling and annealing at 840°C (original sheet) and further alternating bending (AB) in the amount of 0.5; 1, 3 and 5 cycles. Damageability parameters characterizing damage accumulation were determined from the elastic modulus change after the above-mentioned number of AB cycles relative to the values of the elastic modulus in different directions of the original sheet of the studied titanium. The elastic constants of the single crystal and the Kearns texture parameters were used to estimate the elastic modulus in the rolling direction (RD) and transverse direction (TD) of the original sheet, and sheets after an above number of AB cycles. The deviation of the calculated and experimental values of the elastic modulus did not exceed 5%. The deviation of the calculated and experimental values of the ultimate tensile strength and yield stress in the RD and TD both in the initial state and after the corresponding number cycles of the AB did not exceed 10%.