The interaction of a relativistic electron with a dense plasma is studied in the context of inertial fusion fast ignition. Expressions for the electron stopping power and deflection are given and implemented in a three-dimensional (3D) Monte Carlo code. Electron range and penetration depth are computed as functions of the electron energy and plasma parameters; approximate expressions are also proposed. Conditions for fast ignition are studied by including the 3D Monte Carlo code in a 2D hydrodynamic code. The required beam energy is determined as a function of mean electron energy for monoenergetic and exponential energy distributions and a uniform initial deuterium–tritium plasma with a density of 300 g cm−3. A simple model is shown to agree with the code.