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Knowledge of the in situ stress state of rock mass is fundamental for engineering, geological and geophysical applications. In situ stress state determination requires in principle the evaluation of the three principal stresses and the related principal directions, but it is widely recognized in the literature that the maximum horizontal stress is the most difficult component to accurately estimate. In the context of borehole methods, this paper proposes a step-by-step analytical procedure to estimate some bounds to the maximum horizontal stress, starting from a geomechanical description of the rock and relying on information generally available in the engineering practice. The procedure is divided in substeps, each one requiring additional information about the mechanical properties of the rock and on the geometrical properties of the failed portion of rock: more information available implies a lower uncertainty on in situ stress estimate. Furthermore, since the proposed procedure is analytical, it allows a complete and very easy implementation in a spreadsheet. The aim of the work is thus to provide a rigourous but simple analytical tool that can be used in engineering practicte to estimate some bounds to the maximum horizontal in situ stress state. The approach is finally validated by means of both numerical simulations, performed with a sophisticated numerical tool, and experimental field data coming from the literature.