The crystallographic texture and mechanical characteristics (ultimate strength, yield strength, and relative elongation) during tensile tests of Inconel 718 alloy samples are studied. Appropriate samples obtained by 3$D$-printing in the horizontal ($XY$) and vertical ($Z$) directions by the method of selective laser melting (SLM) of the PREP and VIGA powders are studied. The texture of the studied samples is characterized by the fact that the main crystal orientations are located along the [001]–[111] side of the stereographic triangle with the maximum values of the orientation density in the <533> and <100> poles. The magnitude of the maxima and dispersion of crystal orientation depends on the direction of sample construction and the type of post-printing processing. The formation of the texture component <100> is probably because columnar crystals grow fastest, in which the orientation forms a minimum angle with the direction of the greatest heat removal. In alloys with an f.c.c. lattice (which also includes the Inconel 718 alloy), the [111] orientation deviates from the [001] crystallographic direction by 54°. As a result, after selective laser melting in the 3$D$-printing process, the crystallization of grains with [111] orientations can be suppressed by any neighbouring grains of other orientations. It is probably for this reason that, on the reverse pole figures, the pole density <111> is low, and the pole densities <533> and <100> are relatively high. The total density of crystal orientations along the [001]–[111] side of the stereographic triangle for horizontal samples is higher than for vertical ones. At the same time, it is established that the strength properties of horizontal samples are also higher than those properties of vertical ones, and accordingly, the plastic characteristics of horizontal samples are lower than those properties of vertical ones. In addition, the strength characteristics of the samples obtained using the VIGA powder, as a rule, exceed the corresponding values in the samples based on the PREP powder that may be due to the different morphology of the powders used. Correlation analysis of the relationship between texture parameters for samples in the horizontal and vertical directions of construction directly after 3$D$-printing and post-printing processing, on the one hand, and the corresponding characteristics of strength (strength limit, conditional yield strength) and plasticity, on the other hand, is carried out. It allows linking texture and strength parameters. With its help and the application of regression analysis, a linear correlation with high values of the approximation reliability coefficient (0.64–0.86) is established between texture parameters and mechanical characteristics. Thus, as shown, the observed anisotropy of the aforementioned properties is caused by the crystallographic texture. The rational use of crystallographic texture in the process of manufacturing parts by the method of selective laser melting in the corresponding directions of 3$D$-printing will allow obtaining of parts with an optimal set of properties.