Due to the inherent material non-linearity, the analysis of masonry structures is usually performed relying on numerical models. These can tackle the problem from different perspectives, focusing on the material level, e.g. in the case of block-based models, or on the structural level, e.g. in the case of equivalent frame methods. Material models offer high accuracy in predicting mechanical response. Yet, they are computationally demanding, restricting their application to small-scale engineering problems. Structural models, being characterized by efficiency and reduced computational cost, are thus a common choice, particularly among practitioners. However, the \textit{a-priori} idealization of the structure into macro-elements required by these approaches might be challenging, e.g. in the case of historical structures characterized by geometrical complexity. From this standpoint, continuum models could represent a promising compromise between the two approaches, particularly if enhanced by high performing discretization techniques such as hybrid finite elements. In this contribution, an efficient numerical framework for the nonlinear analysis of masonry structures is proposed. The approach relies on the combination of a novel 8-node hybrid stress finite element and a mechanism-based elasto-plastic continuum model for masonry, with the aim of building a tool characterized by accurate predictions and simple material characterization. The detailed outcomes about the active failure modes offered by the mechanism-based model and the possibility to rely on coarse discretization are key elements of this framework. The proposed approach is tested on several structural examples, aimed at highlighting its potentialities. The efficiency and accuracy of the approach are discussed, also considering comparisons with other state-of-the-art modelling approaches.