The understanding and study of the mechanical behavior of submarine pipes have significant relevance in ocean exploration, allowing the application of these structures in adverse conditions. In this sense, protecting the tube's internal surface is vital for the transportation of corrosive materials, threatening structural integrity. Usually, the external surface is at constant hydrostatic pressure, leading to possible structural failure if the project does not consider all failure modes. Within the framework of Metallurgically Cladded Pipes (MCP) and Mechanically Lined Pipes (MLP), Corrosion-Resistant Alloys (CRAs) are inserted in the internal surface of pipelines. However, they are not typically deemed in the structural analysis as an integrant part of the mechanical resistance for the external load. This work presents an initial analytical proposal to calculate the collapse pressure of concentric tubes incorporating the rigidity provided by the CRA. Tied or frictionless numerical models are assumed to describe the interaction between the two bodies at the interface region. These two scenarios establish the upper and lower boundaries for cases where friction is part of the problem. The methodology applies a least-square minimization function based on nonlinear finite element simulations to extract analytical expressions that estimate the collapse pressure. An effort is made to reduce the number of sensitive parameters involved in the analytical proposals and minimize the complexity of the formulation. This process allows the analyst to visualize which parameters are more relevant in various scenarios. Nevertheless, the main goal is to evaluate how the variables are coupled and develop a methodology that can be adapted to reproduce the analyst's necessities.