Studies have shown that undulating propulsion improves efficiency in unsteady wakes. In this work, the goal is to refine the understanding of thrust generation and low energy expenditure in these unsteady regimes by examining the wake profiles of undulating swimmers. The work is based on using Computational Fluid Dynamics (CFD) to evaluate the unsteady fluid interactions associated with undulation-based propulsion. Numerical accuracy is established using benchmark experiments and refinement studies. The model is then extended to study the wake profiles using shape factors and explore correlating these factors to the mechanical power required for self propulsion. By correlating shape factors to power, we discuss their application to evaluate undulating performance.