Jack up is a mobile unit used for oil and gas exploration and production in offshore fields. On demand, the unit is moved and installed in a given location and used for a period up to 12 months before being un-installed and moved to another location. Due to its mobility and re-usability, when the unit is offered for use in a given offshore location, its suitability in terms of safe operation is evaluated in accordance with the guidelines of Site Specific Assessment (SSA) of jack up. When the unit failed safety assessment criteria, the guideline recommended that it is re-assessed by increasing the complexity of the assumptions and methods used. Reliability analysis theories are one of the frameworks recommended for the safety assessment of the units. With recent developments in uncertainty and reliability analysis of structures subject to stochastic excitation, this study aims at providing a review on the past developments in jack up reliability analysis and to identify possible future directions. The results from literature reviewed shows that failure probabilities vary significantly with analysis method used. In addition, from the variants of reliability analysis approach, the method of time dependent reliability for dynamic structures subject to stochastic excitation have not been implemented on jack ups. Consequently, suggestions were made on the areas that need further examination for improvement of the efficiency in safety assessment of the units using reliability theories.