The common design practice of pressure vessels subjected to variable amplitude loading is based on the application of a linear damage summation rule, also known as the Palmgren-Miner’s rule. Even though damage induced by small stress cycles, below the fatigue limit, are often taken into account in design codes of practice by two-slope S-N curves, the sequential effects of the load history have been neglected. Several studies have shown that linear damage summation rules can predict conservative as well as non-conservative lives depending on the loading sequence. This paper presents experimental results about the fatigue damage accumulation behavior of a structural component made of P355NL1 steel, which is a material usually applied for pressure vessel purposes. The structural component is a rectangular double notched plate, which was subjected to block loading. Each block is characterized by constant remote stress amplitude. Two block sequences were applied for various combinations of remote stress ranges. Three stress ratios were considered, namely R = 0, R = 0.15 and R = 0.3. Also constant amplitude fatigue data is generated for the investigated structural detail which is applied for indirect damage calculations. In general, the block loading illustrates that the fatigue damage evolves nonlinearly with the number of load cycles and is a function of the load sequence, stress levels and stress ratios. In particular, a clear load sequence effect is verified for the two block loading, with null stress ratio. For the other (higher) stress ratios, the load sequence effect is almost negligible; however the damage evolution still is non-linear. This suggests an important effect of the stress ratio on fatigue damage accumulation.