Carbon/carbon composites were developed using PAN based carbon fibres and phenolic resin as matrix in different volume fractions and heat treated to temperatures between 1000℃ to 2500℃. Although both the starting precursors are nongraphitizing hard carbons individually, their composites lead to very interesting properties e.g. x-ray diffractograms show the development of graphitic phase for composites having fibre volume fractions of 30~40%. Consequently the electrical resistivity of such composites reaches a value of 0.8 mΩcm, very close to highly graphitic material. However, it was found that by increasing the fibre volume fraction to 50~60%, the trend is reversed. Optical microscopy of the composites also reveals the development of strong columnar type microstructure at the fibre (matrix interface due to stress graphitization of the matrix. The study forcasts a unique possibility of producing high thermal conductivity carbon/carbon composites starting with carbon fibres in the chopped form only.