Precise control of capacitively coupled radiofrequency (CCRF) plasma reactors is required to achieve desired outcomes in surface functionalisation and material synthesis processes. This necessitates detailed mapping of the large process parameter space and a thorough understanding of spatial and temporal variations of the plasma throughout the reactor. These goals can only feasibly be achieved with accurate numerical modelling. Previous numerical studies of CCRF discharges have implemented a range of simplifying assumptions to improve numerical tractability, such as small electrode spacing, radial uniformity, fewer active species and simplified boundary conditions, while neglecting self‐bias formation. Although this approach is useful in developing the methodology for continuum plasma modelling, it poses challenges for direct comparison with experimental data and for understanding the behaviour of plasma processes employed in the surface treatment of large, complex objects, or the synthesis of nanoparticles. Here we report the development of a two‐dimensional axisymmetric continuum model for a CCRF reactor with a pure argon 13.56‐MHz discharge using the finite element method. The large electrode spacing and reactor design result in two distinct discharge regions and the formation of a strong DC self‐bias on the powered electrode. The plasma discharge is studied as the pressure is varied from 0.1 to 0.3 Torr, over the radiofrequency input power range of 25–100 W, which leads to consistent enhancements of the electron density and self‐bias. The impact of the electron energy distribution function (EEDF) on the discharge is assessed, with the assumption of a Druyvesteyn EEDF resulting in a bulk electron density and temperature of 3.4 × 1015 m−3 and 3.3 eV, respectively, compared with 8.1 × 1015 m−3 and 1.9 eV in the Maxwellian case. The asymmetric power distribution throughout the reactor is quantified to build a reduced domain model with a lower computational cost. The effect of an electrically floating parallel plate electrode is assessed, resulting in a 42% higher bulk plasma potential as compared with the grounded case. The inclusion of resonant and 2p excited states of argon is shown to have a major impact on the discharge dynamics, leading to an order of magnitude reduction in bulk electron density. This study proposes a robust numerical model of a CCRF argon plasma discharge to facilitate future simulations of more complex discharges with important implications in plasma surface engineering and synthesis of materials.