The multiple reciprocity method (MRM) boundary variation equation, planar solution expression and well - posedness of Boundary Value Problem of Equation Δu+ku=0;inΩ∪Ω′∈R，u|Γ=u0are derived. This proves the existence and uniqueness of the (MRM) boundary variation equation. It is manifested that the multiple reciprocity method (MRM) boundary variation equation only contains the weak singular integral kernel and there is no any polynomial to be added to the expression of solution. Therefore, it is unnecessary to introduce the Lagrange multipliers in finding the solution, which provides a great convenience for the boundary element numerical solution process.