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Plate and Shell Heat Exchangers (PSHE) are vital in industries due to their adaptability and efficiency. This study applied the finite element method to analyze PSHE plate behavior, which is challenging to assess experimentally. The equivalent von Mises stress field was determined for four-plate setups under different conditions: internal channel pressure, external channel pressure, and pressure in both branches. Peak stresses were found at corrugation tops during contact, varying stress levels based on operating conditions. Stresses decreased when both branches were pressurized but increased with single-branch pressurization. Internal and external pressure-only scenarios had distinct stress patterns. The chevron angle and corrugation contact points influenced plate stiffness and stress distribution. A fatigue analysis assessed plate lifespan under cyclic loads, with fatigue strength reduction factors applied according to Soderberg, Goodman, and Gerber failure criteria. This comprehensive analysis provides critical insights into PSHE plate performance, aiding in their reliable application in the industry. All numerical data obtained in this work were validated based on experimental studies previously published in the literature for stress and fatigue analysis. • The structural behaviour of PSHE was evaluated through finite element analysis. • Results indicated that peak stress occurred in the contact region, but only the outer weld suffered leakage due to fatigue. • Loading the internal and external channels reduced the stress in the contact area. • Numerical results were validated with previously published experimental data, with deviations within 20% for most points. • The fatigue life was estimated with a deviation under10.4 % to experimental data using the fatigue strength factor (K f). [ABSTRACT FROM AUTHOR]