Masonry towers and minarets are slender tall structures and highly vulnerable to strong ground motions due to their structural and material characteristics. The paper aims to investigate the effect of vertical ground motion on damage propagations of historical masonry slender tall rectangular stone minarets numerically. The Ulu Mosque minaret with height of 42.90 m constructed in 639 in Diyarbakir, Turkey, is selected as an application. Firstly, three dimensional solid and continuum finite element models of the minaret are obtained from the surveys. Since the foundation of the minaret is sitted on the hard soil, soil-structure interaction is not considered in the finite element model. The finite element model of the minaret is updated by modal analyses results and an empirical frequency formulation developed using the measurement results. Mechanical material properties of the masonry unit are determined using the properties of the stone and mortar used in the minaret. Concrete damaged plasticity (CDP) material model adjusted to masonry structures is considered in the nonlinear analyses. The acceleration records of horizontal (N-S) and vertical (V) components of May 1, 2003 Bingol earthquake (Mw = 6.4), which was recorded in hard soil and occurred in the near region of Diyarbakir city, are chosen as a strong ground motion. Then, linear time history and nonlinear step by step seismic analyses of the minaret are implemented for only horizontal, and combined horizontal and vertical components of the earthquake. The time histories of displacements, minimum and maximum principal strains and stresses, and damage propagations on the minaret are compared for only horizontal, and combined horizontal and vertical load cases including self-weight. It can be stated that consideration of vertical ground motion component in combination with horizontal component affects damage percentages and propagations on slender tall rectangular stone minarets.