The cellular endocytosis of nanoparticles (NPs) is a fundamental biological process with significant potential in biomedical applications. However, a comprehensive understanding of the mechanistic aspects of endocytosis and the impact of particle properties on this process remains elusive. In this study, we investigated the membrane-wrapping behavior of soft NPs (SNPs) with varying rigidities using theoretical calculations. Our findings reveal that the membrane-wrapping process of SNPs involves a complex energy change including the possible existence of an energy barrier; moreover, it is found that the location and height of this barrier strongly depend on the mechanistic properties of the NPs and membranes. Additionally, by considering force balance in the membrane-wrapping process, we calculated the speed at which NP is internalized by the membrane, showing a nonmonotonic dependence on particle rigidity and/or wrapping degree. These phenomena can be attributed to competition between different energy components associated with NP-membrane binding, membrane tension, and deformations occurring during SNP-membrane interaction processes. Our results contribute to a deeper understanding of cellular-level endocytosis mechanisms and offer potential applications for soft NPs in biomedicine.