The invasion of red blood cells (RBCs) by malaria parasites is a complex dynamic process, in which the infected RBCs gradually lose their deformability and their ability to recover their original shape is greatly reduced with the maturation of the parasites. In this work, we developed two types of cell model, one with an included parasite, and the other without an included parasite. The former is a representation of real malaria-infected RBCs, in which the parasite is treated as a rigid body. In the latter, where the parasite is absent, the membrane modulus and viscosity are elevated so as to produce the same features present in the parasite model. In both cases, the cell membrane is modeled as a viscoelastic triangular network connected by wormlike chains. We studied the transient behaviors of stretching deformation and shape relaxation of malaria-infected RBCs based on these two models and found that both models can generate results in agreement with those of previously published studies. With the parasite maturation, the shape deformation becomes smaller and smaller due to increasing cell rigidity, whereas the shape relaxation time becomes longer and longer due to the cell's reduced ability to recover its original shape.