Fracture of brittle and quasi-brittle solids subject to uniaxial compression has been a challenging topic for decades with little dispersed progress. No well-defined solution for this problem was developed until the day this thesis was finalized. In this thesis, the differences between fracture in compression and in tension are explained making the later a straightforward problem to tackle and form a well-defined commonly-used solution. Exploratory experiments were conducted to gather experimental measurements required for realistic numerical simulation and to confirm that a big void in a compressed brittle/quasi-brittle solid will act as a stress raiser and trigger crack propagation. A 2D numerical model was developed using the material properties collected from the experiments. For a discontinuity to have that effect in a uniaxially compressed brittle solid it needs to have a width and height; a one-dimensional hairline crack is ineffective. The effect of varying initial voids geometry was studied in the first parametric study presented in this thesis. The width (direct relationship), height (inverse relationship), size (direct relationship) and shape of the void are shown to be important in triggering crack propagation, but not the width-to-height ratio. Vertical elliptical voids were found to be less critical than all the other voids studied. In the second parametric study, the effect of a secondary void neighbouring a bigger main void is studied, with both voids being circular to resemble air bubbles. Agreement between the modelled crack paths and cracks observed in the experiments was found, explaining why some cracks emanate from the sides of bigger voids. The findings presented in this study are eye-opening to the reason why research progress in the field has been very slow compared to other topics of Fracture Mechanics.