Reduced-resistive magnetohydrodynamics (MHD) models are used in understanding different phenomenon in various domains, for example, astrophysics to model magnetotail or for solar arcades [Finn Bozkaya JM, Guzdar PN. Loss of equilibrium and reconnection in tearing of two dimensional equilibrias. Physics of Fluids B 1993; 5:2870–2876], modeling plasma confinements in reverse field pinch [Strauss HR. The dynamo effect in fusion plasmas. Physics of Fluids 1985; 28:2786–2792] and tokamaks [Strauss HR. Reduced MHD in nearly potential magnetic fields. Journal of Plasma Physics 1997; 57(1):83–87; Freidberg J. Plasma Physics and Fusion Energy. Cambridge University Press: Cambridge, 2008]. In this context, recently, a new generalized reduced-resistive MHD model, which can make use of an arbitrary density profile was proposed [Després B, Sart R. Reduced resistive MHD in Tokamaks with general density. ESAIM: Mathematical Modelling and Numerical Analysis 2012; 46(5):1081–1106. EDP Sciences, SMAI, 2012 online 2011]. We in this work show that this proposed theoretical model can be realized numerically as well, and that it is very robust if the equation set is written in a very particular form using the properties of FEM. To illustrate these points, we pick the current hole configuration [Fujita T, Oikawa T, Suzuki?T, Ide S, Sakamoto Y, Koide Y, Hatae T, Naito O, Isayama A, Hayashi N, Shirai H. Plasma equilibrium and confinement in a tokamak with nearly zero central current density in JT-60U. Physical Review Letters 2001; 87(11):245001; Hawkes NC, Stratton BC, Tala T, Challis CD, Conway G, DeAngelis R, Giroud C, Hobirk J, Joffrin E, Lomas P, Lotte P, Mailloux J, Mazon D, Rachlew E, Reyes-Cortes S, Solano E, Zastrow K-D. Observation of zero current density in the core of JET discharges with lower hybrid heating and current drive. Physical Review Letters 2001; 87(11):115001], which was modeled using reduced-resistive MHD and remodel it using different combinations of current sources and density profiles. Our model can be implemented with reasonable computational resources at the price of solving a well-posed global linear system and it is unconditionally stable. These features are also demonstrated as a part of our numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.