Silicon-on-insulator is an attractive choice for developing mid-infrared photonic integrated circuits. It benefits from mature fabrication technologies and integration with on-chip electronics. We report the development of SOI channel and rib waveguides for mid-infrared wavelengths centered at 3.7 μm. Propagation loss of ~1.44 dB/cm and ~1.2 dB/cm has been measured for TE and TM polarizations in channel waveguides, respectively. Similarly, propagation loss of ~1.39 dB/cm and ~2.82 dB/cm has been measured for TE and TM polarized light in rib waveguides. The propagation loss is consistent with the measurements obtained using a different characterization setup and for the same waveguide structures on a different chip. Given the tightly confined single-mode in our 400 nm thick Si core, this propagation loss is among the lowest losses reported in literature. We also report the development of Ge-on-SOI strip waveguides for mid-infrared wavelengths centered at 3.7 μm. Minimum propagation loss of ~8 dB/cm has been measured which commensurate with that required for high power mid-infrared sensing. Ge-on-SOI waveguides provide an opportunity to realize monolithically integrated circuit with on-chip light source and photodetector.