A continuum crowd flow model is solved using the Lagrangian coordinate system. The system has proven to give computational advantages over the traditional Eulerian coordinate system for (one- dimensional) road traffic flow. Our extension of the model and simulation method to (two- dimensional) crowd flow paves the way to explore the advantages for crowd flow simulation. This paper provides a first exploration and shows that a model and simulation method for two-dimensional crowd flow can be developed using Lagrangian numerical techniques and that it leads to accurate simulation results.