The Eulerian-frame extraction of pressure fields from particle image velocimetry and particle tracking velocimetry has been thoroughly investigated in the literature. In this thesis, a novel pressure-extraction technique is developed for the extraction of pressure fields in the Lagrangian frame, in which the data is distributed randomly throughout the domain. This technique uses a Poisson solver to extract the pressure field on a network of particles that is constructed using the Delaunay triangulation and the Voronoi tessellation. Using synthetic data, the Lagrangian technique was shown to out-perform the Eulerian technique with the Dirichlet boundary condition. An experimental validation of the technique was performed by extracting the pressure field on the surface of a sphere in free-fall. Comparing the extracted surface-pressure distribution to reference data yielded a good agreement. It is concluded that operating in a purely-Lagrangian frame is advantageous compared to interpolating Lagrangian data to a structured grid.