The paper presents a numerical modelling of fatigue crack initiation in thermally cut structural elements by using improved Tanaka–Mura crack nucleation model. The main goal of the study is to analyse the influence of different grain orientations generated with Voronoi tessellation on the crack initiation period. The numerical modelling of the crack initiation period is performed on the test specimens made of high strength steel with martensitic microstructure. Because the specimens are assumed to be thermally cut without any additional treatment, surface roughness is taken into account in the numerical simulation. Several computational analyses with different grain orientations are performed on the each stress level. Therefore, the stress cycles interval [N1, N2] in which the crack is expected to be initiated with the probability P(N) is determined by using statistical analyses of obtained computational results. Experimental testing is also performed on the uniaxial test machine by stress ratio R = 0.1.