In this paper, we report for the first time on the theoretical and experimental investigation of FeSiB amorphous glass-coated nanowires by analyzing samples with the same diameters in both cases. The hysteresis curves, the dependence of the switching field values on nanowire dimensions, and the effect of the magnetoelastic anisotropy on the magnetization processes were analyzed and interpreted to explain the magnetization reversal in highly magnetostrictive amorphous nanowires prepared in cylindrical shape by rapid quenching from the melt. All the measured samples were found to be magnetically bistable, being characterized by rectangular hysteresis loops. The most important feature of the study is the inclusion of the magnetoelastic anisotropy term that originates in the specific production process of these amorphous nanowires. The results show that the switching field decreases when the nanowire diameter increases and this effect is due to the reduction in anisotropy and in the intrinsic mechanical stresses. Moreover, the obtained results reveal the importance of factors such as geometry and magnetoelastic anisotropy for the experimental design of cylindrical amorphous nanowires for multiple applications in miniaturized devices, like micro and nanosensors.