Several problems in the theory of photon migration in a turbid medium suggest the utility of calculat- ing solutions of the telegrapher s equation in the presence of traps. This paper contains two such solu- tions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher s equa- tion represent an interpolation between wavelike and diffusive phenomena, they will exhibit discontinui- ties even in the presence of traps. The use of a similar mathematical formulation in the design of studies of the scattering and absorption of laser radiation from human tissue (9,10) suggests that it is of some interest to study properties of the telegrapher's equation, rather than the diffusion equation, in the pres- ence of one or more absorbing boundaries. There is little literature related to the telegrapher's equation in the presence of either absorbing or reflecting boundaries. An expression has been found for the mean first-passage time of a particle, whose motion can be described by a telegrapher's equation, to escape from a finite interval (11). In the present paper we derive the solution of the telegrapher's equation for the probability density of the displacement of a particle diffusing on a line in the pres- ence of one and two absorbing boundaries. The solution of the second of these allows one to calculate the survival probabilities for the same systems, and thereby recover the results of Ref. (11). A more interesting qualitative feature to our solutions is the appearance of discontinui- ties in the concentration profile in the presence of traps, which illustrates the fact that the telegrapher's equation can be regarded as an interpolation between the wave and diffusion equations. Our analysis is for the case of a one- dimensional process since there is no unique multidimen- sional extension.