The objective of this study consists in elaborating computational procedures to analyze durability of structural elements with crack-type defects under remote alternating loads. The novelty of the proposed method consists both in applying new benchmark tests for crack propagation analysis, and analyzing structure durability for structure elements with different defects. The problem of the stress intensity factor estimation for mode I loading is reduced to solution of a hypersingular integral equation. Analytical solutions of this equation with different right parts are obtained for penny-shape cracks. It is the basis for verifying boundary-type numerical methods. The problem of determining the number of cycles to failure for structural elements subjected to cyclic loading (tension-compression) with a given frequency and amplitude is solved. The Paris dependence for fatigue crack growth has been used to determine the critical number of cycles before failure. Numerical results characterizing the durability of structural elements with crack-like initial defects have been accomplished.