We consider a multiple vehicle path planning problem with curvature constraints in the presence of obstacles, where multiple vehicles need to arrive at a given final location simultaneously. We aim to find the paths using a simplex framework that tessellates the feasible regions into hexagonal grids from which a graph is abstracted with nodes at the mid-point of every hexagon edge. The graph edges are defined over the adjacent nodes of the hexagons and each edge corresponds to a quadratic Bezier curve. We present an algorithm that finds the shortest path for each vehicle, and a path perturbation technique to make the path lengths equal with in a given error tolerance. We test the proposed approach using simulated scenarios and present the results.