The relationship between the flux-trapping phenomenon and the device-structure of a SQUID has been studied using three types of SQUIDs; a SQUID with a guard-ring, a SQUID with a moat, and a SQUID without these structures. The change in the voltage-flux characteristics of the SQUIDs due to the flux-trapping are measured. For the measurements, an acceleration of the flux-trapping is realized by applying a magnetic field during cooling of the SQUIDs. From the measured results, the SQUID with the guard-ring and that with the moat can reject tha external magnetic field more effectively than the SQUID without these structures. The reason of the difference in the rejection of the external magnetic field is thought to be the existence of superconducting closed loops. However, the flux-trapping of the SQUID with the guard-ring and that with the moat occur more easily than the flux-trapping of the SQUID without these structures for the cooling under the finite magnetic field. Therefore, the moat structure and the guard-ring structure need a higher-grade magnetic shielding for a practical use.