3-D electrostatic fields are calculated by the linear interpolation triangular boundary element method (BEM) with analytical integrals.For integrals with 1/R and 1/R²,shape functions are disintegrated into constant,x linear and y linear terms.The boundary element integral is simplified to 6 basic integral assemblies.Analytical integral formulas for them are introduced.Repeat calculations resulting from different shape functions are avoid.The method calculates exactly integrals far from singularity, 1 and 2 order nearly singular integrals and 1 order singular integrals as well.It shows that for problems with nearly integrals and singular integrals the analytical integral method gives correct results while the numerical integral method with the same boundary meshes can not.The precision in linear interpolation BEM for 3-D electrostatic fields is improved.