An elliptical artificial boundary is introduced in the hybrid finite element method-analytical approach (FEM-ANA) for open boundary 2-D electromagnetic problems. It includes, as a special case, the circular artificial boundary (CAB) of Chari. The new artificial boundary (AB) is more flexible close to the configuration of the interested region than CAB, and makes the computation region of FEM reduced; meanwhile, it enlarges analytical solution region. The cost of the analysis of the exterior region for the two ABs is almost the same. The proposed approach is applied in analysis of electrostatic field and eddy current field problems.