Diode-laser pumped monolithic single-frequency non-planar ring laser has the advantages of compactness, reliability and high efficiency. But when the pump power is high enough, the thermal effect will be serious and the high-order transverse modes will appear. Therefore the single-mode output power is limited. In this paper, the mechanism of generating the high-order transverse modes in the monolithic unidirectional non-planar ring cavity is analyzed using ray tracing method. The calculated results are in agreement with the experiments.