[en] The new universal algebraic variational-iterative method (AVIM) to solve problems of electrostatics for any system is developed. Potentials of their elements satisfy the Laplace equation Δφ (r)=0. The method is based on a simple and accurate algorithm and on the well- known formula for the potential at any required point Φ=Q/4πεr. In comparison with the standard approaches to the Laplace equation through the Dirichlet or Neiman problem, the developed method does not require to apply complex methods of mathematical physics. The boundary problems of electrostatics are solved numerically only by algebraic variational-iterative calculations. The required potentials, electrical fields, the surface charge density of the system elements are obtained by linear superposition of potentials and electrical fields created by the system of point changes. All charges are located inside the conducting elements of the system, their values are defined as a result of iterative process providing performance of boundary conditions with the necessary accuracy. (author)