A numerical code, labeled InCa4D, used for simulating CPU-efficiently the guiding of charged beam particles through insulating straight nano or macro capillaries, is presented in detail. The paper may be regarded as a walk through the numerical code, where we discuss how we compute the charge deposition and charge dynamics at the interfaces of a straight capillary and how we compute the electric field with imposed boundary conditions. The latter add surface polarization charges at the dielectric interfaces and free charges at conducting interfaces. Absorbing boundary conditions allow for a leakage current. As a result, the electric field in InCa4D yields accurate relaxation rates and decay rates for both cases, namely where the outer surface of the straight capillary is covered by a grounded conducting paint or not. Eventually, we show how we sample the initial conditions of the inserted beam particles and how we evaluate CPU-efficiently the particles’ trajectory, allowing to compute typically 106 trajectories in about two hours on a modern CPU.