Abstract This article introduces the R 2 Fill method, which is an algorithm for filling a region with particles isotropically. The method's isotropy is tested geometrically and then mechanically with the Discrete Element Method (DEM). It applies to planar and three‐dimensional problems and is simpler to implement and has competitive metrics compared to other Advancing Front packing algorithms. The DEM formulation used in this paper provides a way to model solid materials and eliminate residual stress created in any particle packing algorithm. The R 2 Fill method was tested over ranges of particle sizes. At large size ranges the method generated a higher coordinate number and denser particle packing, with 79.718% fill at the maximum tested size range. The geometric isotropy was improved at higher size ranges yielding less than a 1% isotropic error. The method also had fewer particles than the similar and more complex algorithm by Yongjun Li. Lastly we tested mechanical isotropy by using our DEM formulation to measure the stress–strain response under a tensile load at different orientations. The R 2 Fill method produced mechanical isotropy within 2% error for the elastic moduli, shear moduli, and Poisson ratio.