We present a numerical spectroscopic study of visible and infrared laser radiation in a biological tissue. We derive a solution of a general two-dimensional time dependent radiative transfer equation in a tissue-like medium. The used model is suitable for many situations especially when the external source is time-dependent or continuous. We use a control volume-discrete ordinate method associated with an implicit three-level second-order time differencing scheme. We consider a very thin rectangular biological-tissue-like medium submitted to a visible or a near infrared light sources. The RTE is solved for a set of different wavelength source. All sources are assumed to be monochromatic and collimated. The energetic fluence rate is computed at a set of detector points on the boundaries. According to the source type, we investigate either the steady-state or transient response of the medium. The used model is validated in the case of a heterogeneous tissue-like medium using referencing experimental results from the literature. Also, the developed model is used to study changes on transmitted light in a rat-liver tissue-like medium. Optical properties depend on the source wavelength and they are taken from the literature. In particular, light-transmission in the medium is studied for continuous wave and for short pulse.