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• The effect of size on molecular dynamics simulation results are considered. • Tensile and shear properties of amorphous silicon nitride with different densities calculated using molecular dynamics simulations. • The empirical equation between mechanical properties (Young's modulus, shear modulus, tensile strength, and shear strength) and density of amorphous silicon nitride is established. Silicon nitride fiber is among the most popular candidates for high-temperature wave-transparent ceramic matrix composites (CMC) in aerospace engineering, and the measurement of its mechanical properties has always been the focus of researchers. In this paper, a simple and effective molecular dynamics method is used to generate molecular dynamics models of amorphous silicon nitride (a -Si 3 N 4) materials with different densities, and it is verified that the developed models reflect the microstructure of the fiber. Based on analyzing the effects of size on the results, tensile and shear simulations are carried out to obtain the mechanical properties of the models with different densities. According to the research data obtained, the empirical equation between mechanical properties (Young's modulus, shear modulus, tensile strength, and shear strength) and density of fiber is established, and validated by the published experimental results. The empirical equation can not only predict the mechanical properties of fibers directly from the density but also provide a new way to measure the mechanical properties of fibers nondestructively. [Display omitted] [ABSTRACT FROM AUTHOR]