This work concerns the stability of unreinforced masonry slender circular cross-sectional columns subjected to their own weight and eccentric vertical load. Cantilever columns are examined, considering that the material has infinitely linear elastic behavior in compression and has no tensile strength. For the analysis, an existing numerical model and solution procedure developed for the stability analysis of masonry elements with rectangular cross-section are utilized and adapted to the circular columns. For the instability of the columns, an appropriate criterion that relates the top lateral deflection to the intensity of the applied eccentric vertical load is employed. By considering a reference column, critical buckling load is obtained, behavior of the column interpreted and efficiency of the numerical model emphasized. Performing a nonlinear buckling analysis using a general purpose software on this reference column, obtained results are compared with those of the adapted procedure of the present study. Implementing parametric analyses on reference column, effects of the column slenderness, eccentricity of vertical load, elastic modulus, and self-weight on the buckling load are investigated. Presented calculation procedure provides a useful tool in order to calculate the critical loads or to check the stability of masonry circular columns.