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In this paper, a numerical approach for the pushover analysis of masonry towers, having hollow arbitrary sections, is proposed. Masonry is considered a nonlinear softening material in compression and brittle in tension. The tower, modeled in the framework of the Euler-Bernoulli beam theory, is subjected to a predefined load distribution, but the problem is formulated as a displacement controlled analysis in order to follow the post peak descending branch of the structural response. Nonlinear geometric effects and nonlinear constraints (the latter due to surrounding buildings) are also considered. Benchmarking pushover analyses are performed with the commercial code Abaqus in relation to a real case (the Gabbia Tower in Mantua), which proved the accuracy and reliability of the results obtained with the present formulation and the noteworthy reduction of computing time. [ABSTRACT FROM AUTHOR]