Power plant components may be subject to severe ranges of pressure and temperature when in-service. As a result, significant pressure and thermal stresses may occur which are cyclic in nature. For such components it is necessary to demonstrate an acceptable creep and fatigue life. However, before any such assessment can take place it must first be demonstrated that the cyclic loading would not lead to incremental plasticity, also known as ratcheting, and ultimately plastic collapse. If ratcheting does occurs then the calculation of creep and fatigue lives based upon a steady cyclic behaviour is invalid. It is therefore useful for find out how close structures are to ratcheting. A power plant tubeplate has been analysed using non-linear finite element methods to assess its susceptibility to ratcheting and the potential for plastic collapse to occur. This is referred to as a shakedown assessment. Finite element analysis is a traditional method for assessing shakedown, however this approach is computationally expensive. An alternative method of assessing shakedown, which is significantly more efficient, although not as well validated, is the Linear Matching Method. In this work, both finite element analysis and the Linear Matching Method have been used on a real world problem. The objective of this work is to assess the advantages and disadvantages of the LMM when compared to traditional non-linear finite element methods.