In the method, grippers are placed on a stationary assembly table and rod-like members forming a wooden construction are laid on the support of said grippers. The wooden construction can be for example a roof truss or a wall frame. The assembly table comprises a vertical fastening plane to which the grippers are fastened. The fastening plane can be made of ferrous material and the grippers can be fastened to the fastening plane magnetically or by means of a suction pad gripper. The fastening of the grippers to the fastening plane, the fastening of the rod-like members to the grippers and the joint connecting the rod-like members are conducted by means of an assembly robot. The joint may be a nail plate joint, a nail, screw or staple joint or a glued joint. From the CAD file of the wooden construction a list of commands controlling the operation of the assembly robot is generated by means of a decompression program. The grippers belonging to the apparatus comprise first grippers and second grippers. The first grippers comprise a frame to be fastened to the fastening plane and a supporting part fastened to the frame. The supporting part comprises a face supporting surface to be positioned against the face of the rod-like member, an edge supporting surface to be positioned against the edge surface and a pivot plate for pressing the rod-like member against the face supporting surface. The second grippers comprise a frame to be fastened to the fastening plane and a gripping bracket. The gripping bracket comprises a grip surface to be positioned against the face of the rod-like member, a lip to be positioned against the edge surface, as well as a gripping member, such as a suction pad, for adhering to the surface of the rod-like member.