Annihilation of slow positrons at a polymeric surface has been discussed in terms of positron diffusion and trapping of positronium into free volume holes. The above model has been used to calculate the ortho-positronium lifetime (τ 3 ) in polystyrene (PS), epoxy resin film, polyurethane (PU) and polytetrafluroethylene (PTFE) as a function of temperature, incident positron energy and mean implantation depth. The results have been compared with the experimental observations of other authors. The variation in τ 3 with respect to temperature clearly demonstrates a discontinuity in the curve at T g corresponding to the glass transition temperature. The variation of calculated τ 3 shows that the lifetime increases significantly above T g however, below T g it increases only slowly. This is a direct consequence of the change in the size of free volume holes. The T g has been found to be dependent both on positron energy and density of the polymer. Large variation in τ 3 has been observed at low energies suggesting a significant structure of free volume holes near the surface.