Low-pressure dc wire induced plasma sources exhibit two stable modes of discharge—constricted below a threshold pressure and diffuse above. Starting from experimental measurements, we conduct two-dimensional particle in cell (PIC) modelling of a dc low-pressure (10⁻⁴–10⁻² mbar), low-current (∼1 mA) wire discharge in helium. 2D PIC modelling is required to capture longitudinal non-uniformity of the diffuse mode. PIC simulations reproduce the two discharge modes. The voltage versus pressure curve obtained from simulations matches fairly well the experimental data, including the transition region. Discharge voltage dependence on pressure is analysed in consideration of electron impact ionization rates' evolution with energy. In light of the PIC findings, a model of the discharge mode transition based on the Child–Langmuir theory for ions is proposed. Confrontation with simulated data shows good agreement and validates the model for mode transition prediction. Simulations show that the diffuse mode is a space-charge-dominated regime.