At this present time, oil and gas reservoirs are found in challenging locations and can be reached at depths which were impossible to achieve a few decades ago. In order to reach these reservoirs, both state of the art technology and a great knowledge are required. Geomechanical problems are just one issue which may occur during drilling operations. In situ rock properties evaluation is an important element of geomechanical analysis, which helps in understanding principles such as wellbore stability, bit selection, BHA design, hole quality, stuck pipe studies and drilling dynamics. Drilling dynamics is another phenomenon, which is not well understood and can substantially increase costs, Non-Productive Time ("NPT") and failures. All this knowledge is crucial for the successful drilling of directional, highly deviated and horizontal wells. This thesis focuses on rock strength modelling with the use of logs to enable an estimation of in situ rock properties from sonic, density or another log. Sandstone and limestone rock samples were acquired for this thesis, which were subsequently cored into five centimetre cylinders. Primary wave velocity was measured and a Uniaxial Compressive Strength ("UCS") test was carried out on both samples. As a result, the acquiring process is given and recommended usage described. Drilling dynamics can lead to dysfunctions, such as full stick slip, low or high torsional oscillation, bit whirl or random torsional oscillation. All of these are dependent on BHA design, surface drilling parameters and rock properties. All of these phenomena are investigated in this thesis and, as a result, recommendations and best drilling practices are given.