Over the past years OMV experienced several incidents on its drilling rigs related to dropped blocks. There was severe damage to the equipment but luckily nobody was harmed. The incidents were all related to improper maintenance, wrong usage of equipment and insufficient crew competence. A literature research has been conducted, to get information on the design and function of the different drive and brake systems which are used on rigs nowadays. The main focus upon investigation and determination of Safety Critical Elements is the drawworks system with its main and auxiliary brake system and the drive system on alternate current driven rigs, which can be equipped to feed back energy to the rig system and thus reducing the block speed. To identify Safety Critical Elements of the brake and drive system the incident investigation reports from OMV were analysed and furthermore Safety Alerts from the International Association of Drilling Contractors (IADC) and other regulating institutions were taken into consideration. The retriefed results were put into a Failure Mode and Effects Analysis and the risk priority numbers for each element were evaluated together with a team of long yeared specialists from OMV. The analysis of the results showed that crew competence and insufficient crew training is the main root cause for the incindents regarding to OMV contracted rigs next to insufficient maintenance and management systems. Opportunities to mitigate these root causes are given in this thesis to reduce the risk of reoccurrence. Further methods to monitor and measure the brake performance of every system are shown to ensure to choose an adequately moment for maintenance and inspection of every system.