In this work, an approach based on the Virtual Crack Closure Technique, included in the commercial finite element code ABAQUS, is adopted to study the propagation of delamination in composite structures under quasi-static and fatigue loads. The methodology, originally capable of simulating only delamination under quasi-static loads, has recently been extended introducing the possibility to analyze damage progression under fatigue load condition. The approach is assessed on simple specimens, Double Cantilever Beam and Mixed Mode Bending test, comparing the results with literature data. Afterwards, the behavior of a single-stringer specimen with an initial delamination is numerically investigated considering compressive loading conditions. At first, the single-stringer specimen is analyzed under quasi-static compressive load showing a clear correlation between local buckling phenomena and delamination growth. Then, a cyclic compressive load is applied such that the specimen switches between pre- and post-buckling conditions in a single load cycle. The outcomes of the numerical analyses are compared with the experimental data obtained from an experimental test campaign previously performed, showing the advantages of the adopted numerical technique but also the limitations that need to be addressed to properly analyze this phenomenon.