Jellyfish are considered the most energetically efficient swimmers to have ever existed, so their propulsion method can be researched to improve our own underwater vehicle designs. These unique animals need to be very efficient because of their untraditional bodily components, and because most consume limited food while they prey passively during swimming. Jellyfish accomplish their efficiency through vortex propulsion. The contraction of a jellyfish’s bell generates a vortex ring as it swims, which due to its axial symmetry we simplify into two dimensions using two point vortices. We model these vortices using a system of differential equations, for which parameters can be selected to adjust the strength, location, and direction of their rotation. To numerically solve the system, we use the fourth order Runge-Kutta method in MATLAB. The first goal of the project is to examine the jellyfish’s propulsion and maneuvering mechanism, which involves creating simulations for various parameter values in the system of differential equations. Secondly, we study the material transport in the vicinity of jellyfish and its implication on food acquisition. Massless particles are inserted into the fluid flow to observe how the jellyfish and particles around it move through the water as affected by the vortices. To work towards these goals, we have implemented bell shapes to represent moon jellyfish, Pacific sea nettles, cannonball jellyfish, and lion’s mane jellyfish to provide a breadth of bell shapes and sizes. Each of these bell shapes serve as a barrier to material transport, so the jellyfish can capture particles from the surrounding environment. These results have significant implications for fields such as biomimetic engineering, including improvements to sub-aquatic vehicle efficiency and reliability, especially in cases when speed is not a priority.