In geotechnical engineering practice related to mining, tunnelling, and oil exploration, a set of discontinuities might affect the overall strength and stability of rock mass. To address this issue, a good deal of research has been conducted in the past decades to study the behaviour of jointed rocks under different loading conditions. However, most of previous studies have been conducted on rock-like materials such as concrete or plaster, while only limited research has been done on natural rocks. This study seeks to bridge this knowledge gap and (1) to investigate the effects of discontinuity on the engineering properties of common rocks from South East Queensland, and (2) to develop a numerical model that can accurately estimate the strength of jointed rocks. A series of unconfined compression tests on natural rocks of different geological origins (three types of sandstone, argillite, and basalt) were performed to better understand the effect of crack length (1 cm and 2 cm long) and infill material (sand or clay) on rock strength. In addition, a series of shear tests were conducted on jointed specimens of two types of sandstone with different infill thicknesses, ranging from 1mm to 3mm. The obtained results from the laboratory tests were used to improve the current methods of rock shear strength predictions, which were initially designed to estimate the strength of artificial rock-like material. Also, a new numerical method was proposed to accurately estimate the unconfined compressive strength of rock specimens with pre-existing discontinuities filled with either clay or sand. This numerical model provided valuable insight into the failure mechanism of jointed rocks, which agreed with the data obtained in the laboratory. By combining the experimental and numerical investigations, the mechanism of rock failure with different pre-existing cracks and infill material can be studied. The UCS values estimated by the numerical model and the damage model were able to estimate with a high degree of accuracy to the unconfined compressive strength of rocks with pre-existing discontinuities, and it allows to identify and explain the mechanisms of two common damage patterns observed in laboratory tests. The presence of discontinuities (1 cm or 2 cm long cracks) decreases the UCS of natural rocks, while filler material has a tendency to increase the overall strength of the tested rocks.