The mechanical behavior of multiwalled carbon nanotube/epoxy composites was studied in both tension and compression. It was found that the compression modulus is higher than the tensile modulus, indicating that load transfer to the nanotubes in the composite is much higher in compression. In addition, it was found that the Raman peak position, indicating the strain in the carbon bonds under loading, shifts significantly under compression but not in tension. It is proposed that during load transfer to multiwalled nanotubes, only the outer layers are stressed in tension whereas all the layers respond in compression.