The effects of the earthquakes’ vertical component on the damage and collapse of engineering facilities have been long debated. Normal force plays a fundamental role in the strength and stability of masonry buildings, which are thus particularly sensitive to the contemporary application of vertical and horizontal dynamic solicitations. The present work deals with this problem using a masonry-like beam model under the Euler-Bernoulli hypothesis. In this framework, the bending moment and normal force over a beam’s section are nonlinear, invertible functions of both the curvature and elongation of the longitudinal axis. The resulting equations for the beam’s transverse and axial vibrations are coupled. The nonlinear dynamic problem is solved numerically, and some examples are presented and discussed, focusing on the structural typology of masonry towers.