Under the assumption that seismic coda waves may be modeled as a superpositon of single scattered body waves due to scatterers randomly distributed in the three-dimensional earth, we study how nonisotropic scattering and nonspherical source radiation patterns affect the coda wave excitation. The energy density of coda waves is represented by an integral over scattering angle or radiation angle. Properties of each integral kernel are analytically studied in detail. The energy density of coda waves is factored into 2 parts: a geometrical factor and a function of the ratio of the lapse time measured from the earthquake origin time to the travel time of direct wave. The equations predict that the influence of nonisotropic scattering and that of nonspherical source radiation will be significant, particularly on the earth part of coda waves.