Single-longitudinal-mode operation with single-wavelength emission at 1319 nm and dual-wavelength emission at 1319 and 1338 nm is realized by utilizing two types of coating specification for monolithic Nd:YAG lasers. Each longitudinal mode consists of two orthogonally polarized modes. Experimental results reveal that the frequency splitting between two orthogonal polarizations can be tuned by changing the external mechanical force applied on the Nd:YAG crystal. The beat frequency can be linearly varied from 181.3 MHz to 1.64 GHz. The beat frequencies between two orthogonally polarized modes at 1319 and 1338 nm are found to be very close, and their difference can be changed from 4.5 to 19.9 MHz by increasing the external mechanical force from 1.6 to 15 N.