Boundary element method using linear basis function is applied to obtain fields scattered from a 3-D dielectric sphere. Electric field integral equation is used on the surfaces of the dielectric material where its surface is discretized into trilateral cells. For plane wave incidence, scattered fields by a dielectric sphere is calculated and compared with its analytic solution. The diameter and the relative dielectric constant of the dielectric sphere are chosen as 1 meter and 2, respectively, and the wavelength of the incident field is chosen to be 2$\pi$ and 3$\pi$ metres. The total electric fields are calculated on the great circle of the sphere boundary as well as the outside of the sphere in the plane of the wave vector and the polarization vector of the incident electric field. When the size of the trilateral cell is about one thirties of the wave length the error in the numerical calculation result compared with the exact analytic solution is less then one percent for copolaized fields and is less then 4 percent for cross polarized fields.
