We made small superconducting coils and measured the total AC loss under the AC and DC external magnetic fields. The coil winding conditions are that 1, 5, and 10 N of the winding tensions and bobbin materials are glass fiber reinforced plastic (GFRP) and Dyneema fiber reinforced plastic (DFRP). The GFRP and the DFRP have thermal strain properties of contraction and expansion respectively with cooldown to cryogenic temperature. Mechanical losses were estimated from the measured data. According to the estimated mechanical losses, the loss of the coil whose bobbin material is the DFRP was small because the DFRP bobbin expanded and hence the winding was tightly fixed. Approximate 10 to 13% of the AC loss can be reduced by only changing the bobbin material from the GFRP to the DFRP.