A technique combining the plane wave spectrum method and the T-matrix method is used to calculate the internal and scattered electric field intensities of a homogeneous dielectric spheroidal object illuminated with a polarized shaped beam. This technique is modified and used here for spheroidal objects of size parameter and elongation larger than those previously demonstrated in the literature. The beam is modeled using an angular spectrum of plane waves. The beam is physically realizable, satisfies Maxwell's equations and arbitrarily focused. Also the beam can be shifted far a away from the surface of the object. Scattered and internal intensities are calculated using the T-matrix method. The behavior of the internal and scattered field intensities of different spheroidal objects shows that a near resonant mode(s) can be excited in a spheroid illuminated with a focused and shifted beam that propagates in a direction perpendicular to the elongation direction of the spheroid. The axial ratio (ratio of the radii of the spheroid) is a more critical parameter for the internal and scattered field distributions in the case of an oblate spheroid as compared with a prolate case. This technique can be used to calculate the internal and scattered fields of an inhomogeneous layered spheroid illuminated with an arbitrary shaped electromagnetic beam