SPILLMOD is a mathematical model of the evolution of marine oil spills implemented as a software package. A new Eulerian–Lagrangian Computational Fluid Dynamics (CFD) method has been developed for solving shallow-water type equations in a domain with free and contact arbitrary configuration boundaries. A distinctive feature of the model is the ability to calculate the thickness field of oil pollution in the presence of contact boundaries, taking into account the processes of spreading and weathering. When calculating the evaporation of high-viscosity oil types, the factor of damping the evaporation rate due to molecular diffusion of oil components in the liquid phase is taken into account. Calculation of natural dispersion of oil layer is carried out taking into account sea surface conditions, experimental data on oil film crushing in the wave mixing layer and turbulent diffusion in the upper ocean layer, taking into account physical and chemical properties of surface pollution. An additional module in the model is designed to estimate potential spill detection zones. These examples of model application in conditions of real configuration of port water areas and for actually occurred emergency spills demonstrate declared qualities of the model as a tool of information support of oil spill response operations on the sea surface and other water bodies.