This paper presents a new macro-block limit analysis formulation that accounts for non-periodic masonry patterns. The sliding-rocking failure mechanism is parametrised and formulated according to the upper bound limit analysis theorem, coupled with a heuristic solver that is able to minimise the load multiplier and identify the geometry of the appropriate macro-block for the analysis. The proposed formulation introduces the computation of the frictional resistance at the macro-block interface by evaluating the vertical and horizontal lines of minimum trace. These are easy to define by practitioners and to apply in real engineering problems. Finally, the proposed analytical model is implemented by employing an object-oriented coding environment with an a-doc designed user graphical interface, which allows one to parametrically explore all possible failure mechanisms and immediately visualise the effects of the user assumptions. This is particularly suited to support a decision-making process that strongly relies on engineering judgement. The proposed analytical model is verified in a number of case studies by comparing advanced DEM simulations and numerical results arising from the literature.