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The Cell Method (CM) is an approach to the numerical solution of field physical problems that has been recently applied to the electromagnetic computation. It is gaining more and more interest as it allows easy formulations based on integral (finite) quantities, with no need to resort to local quantities related by differential equations to be suitably regularized in numerical form. The paper deals with an application of the CM to the solution of electrostatic problems. Two formulations are presented: The first is suitable for isotropic electrostatic media, and the second is specifically suited for the anisotropic ones. The main items of the method and the structure of the two algorithms are described, and some results obtained for reference cases are reported. A comparison is also shown with the results from a first-order finite element method (FEM) algorithm.