This paper examines the initial transients of the radiation intensity and flux for a one-dimensional semi-infinite medium where the incident source pulse is of the duration of picoseconds or less. As a first approximation the intensity field is modeled as a linear function of the cosine of the angle, and the coefficients of the linear function are functions of time and position. The mathematical form of the resultant radiative transport equations is of a hyperbolic form with a wave speed equal to 1/√3 of the speed of light in the medium. The incident source travels at the speed of light. Applications where these results are important include the transport of femtosecond and picosecond laser pulses through absorbing and scattering medium such as in the imaging of tissues or probing the characteristics of particulate medium by examining the transmitted or back-scattered transients. The speed of light in vacuum is 0.3 mm/picosec or 0.3 μm/femtosec, and therefore corresponding to the duration of a 1 picosec pulse the penetration distance is only 0.3 mm or for a 100 femtosec pulse only 30 μm. The transient term in the radiative transfer equation, usually neglected, is of the same order of magnitude as the spatial derivative in such situations, and cannot be neglected. The results for a one-dimensional medium obtained by the method of characteristics show a distinct wave nature which asymptotes to the diffusion result at large time after the incident pulse has ended. The time dependent reflectivity of the medium can be correlated to the medium properties.