A 3-dimensional macroscopic discharge model in mineral oil is introduced. The process of streamer propagation and branching is simulated between two energized electrodes. The propagation of individual streamer branches in mineral oil is evaluated by using simple physical considerations based on electrostatic calculations performed throughout the discharge development. The simulation is performed by using commercial finite element method (FEM) software in a simulation application. The morphology and the potential gradient change along the streamer perform a good consistency with experimental results. In the paper, the first attempt to validate the model with a "single" guided streamer filament creeping on a glass dielectric under step voltages is presented.