To provide a closing member attachment which prevents environmental pollution due to oil leakage by eliminating the need for exchange of the attachment, and a construction method of a continuous wall.

A closing member attachment includes a support base plate 51 externally attached to a portion of a chuck device 30, a rotation cylinder 52 with both open ends which is rotatably mounted through the support plate 51, and a holding part 60 which is arranged in the rotation cylinder 52 and holds a closing member passing through vertically. The holding part 60 can be rotated together with the rotation cylinder 52. A load can be transmitted among the holding part 60, the rotation cylinder 52, the support base plate 51, and the chuck device 30.