For some special applications, such as SQUID cooling, an entirely nonmetallic coaxial pulse tube cryocooler (PTC) was designed and tested, and the performance of nylon mesh as a regenerator matrix was also investigated. The study of nylon mesh in metallic PTCs shows that nylon mesh is suitable as regenerator matrix in the cold head at temperatures around 80 K. However, the measured performances of cryocoolers using nylon mesh are found to be significantly worse than that using stainless steel mesh. The distorted nylon mesh is considered to be one of the main reasons for the loss in performance. A lowest temperature of 74 K and a cooling capacity of 0.14 W at 80 K has been obtained by our nonmetallic cryocooler. Although the losses of nonmetallic PTC are bigger than the original prediction, there is still a large room for improvement. Such an entirely nonmetallic PTC is an alternative choice for SQUID-cooling without cryogenic liquids.