Over the years, housing has always been one of the basic human needs. Stones, clay, wood and cement are common construction materials. Currently, cement structures are highly solicited both in our country and all over the world. However, cement structures suffer from stress-induced cracks attributed to overloading. The study was carried out to find out the possibility of minimizing the crack formation and increasing the stability of cement structures to fracture. The goal of the study is to characterize the physical and mechanical properties of the cement mortar reinforced with oil palm mesocarp fibers (OPMF) to increase the crack resistance of the structures built with cement mortar, as well as to simulate nucleation and growth of cracks up to the fracture. Composition of the prepared samples differed in the content of OPMF: 0.25, 0.5, 0.75, 1, 1.25, and 1.5 of sand weight. Analysis of the physical and mechanical characteristics of the samples carried out after 7, 28 and 45 days revealed that the rate of water absorption increases in proportion to the increase in fiber content and ranges from 2.4 to 11.6. The three-point bending test was used to determine the flexural strength and Young’s modulus (YM) upon bending. The flexural strength and YM increase as the fiber content of the sample increases from 0 to 0.25 and then decrease. The maximum values of the flexural strength (5.475_MPa) and YM (283.633_MPa) in bending were obtained after 45 days on a sample containing 0.25_% fibers. The compression test was used to determine the compressive strength and YM under compression. The compressive strength and YM decrease with increasing fiber content in the samples. The maximum values of the compressive strength (23.18_MPa) and YM (310.044_MPa) were obtained for the sample containing 0 of fibers. Analysis of the destruction of organic fiber cement samples revealed that the crack propagation occurs by the mechanism of coalescence of micropores. Stochastic modeling carried out for different fiber content showed that the crack growth rate also increases in proportion to the increase in the fiber content. Thus, the main cause of fracture in compressive and bending tests is the viscous growth of the pores and ductile-brittle crack growth through the cement grains.