The collapse of submarine pipelines can have immense economic and environmental impacts, and understanding the mechanical behavior of such structures under extreme external pressure is vital for the design, fabrication, installation, and operation. The pipe's outer surface is susceptible to damage/impacts due to uncontrolled circumstances, possibly leading to structural changes. This work applies numerical tools to evaluate the collapse and buckle propagation in steel pipes, considering the effects of an initial known deformation caused by different puncher's shapes. Therefore, the structure assumes a new geometry leading to modification in the capacity to withstand external pressure. The analysis applies and compares two numerical methods: the arc-length (Riks) and dynamic-explicit approaches. This comparison allows establishing a direct association between the observed features of the two methodologies. In a general manner, the observation indicates that an increasing indentation causes a reduction in the collapse pressure but also significant changes in the propagation pressure. The similar results between the two methods applied in steel pipes permitted extending this concept to estimate the propagation pressure in Mechanically Lined Pipes (MLPs), where the Riks method is unstable, and the dynamic approach is suitable. In this scenario, the possibility of the internal liner buckling before the external backing steel and the appearance of new failure modes is part of a new complex scenario where the number of variables grows significantly, and the collapse circumstances must be reassessed. The boundary conditions, interface state, and other structural parameters increase the difficulty in this type of analysis, showing that in MLPs the number of variables associated with propagation pressure is much higher than in steel pipes.