Laser induced fluorescence is a rapidly growing technique for diagnostics and imaging in scattering material, most notably in in vivo biomedical testing. Most previous applications have relied on the measurements of the steady-state emission spectrum, with subsequent analysis of the spectrum for relative concentrations of potential fluorophores. Only recently a few investigators have explored the use of the fluorescence lifetimes as a diagnostic tool by taking advantage of the perturbation of the lifetime by multiple scattering of the excitation and emission light in the tissue. We have developed a model to study the fluorescence signal generated by fluorophores distributed in a scattering medium. This model is based on two coupled time-dependent photon migration phenomena: the transport of the pulsed source laser light and the transport of the induced fluorescent light excited by the source. The coupling of these two is through the source for the induced fluorescence where the strength of the local fluorescence emission depends on the absorption of the laser intensity at that location. Whereas previous research focused mainly on the fluorescence properties of various dyes, compounds and materials, transport phenomena have only recently been addressed by researchers. We have presented general analytical and numerical solutions for finite, infinite, cylindrical and spherical geometries.