Interaction between granular solids and boundary structures is a fundamental problem encountered in bulk solids handling and subsurface structural design. Current understanding of its mechanism has not been adequate for robust and economical engineering designs, especially for flexible boundary structures. A classic and essential example is uniaxial compression of dry granules in a deformable cylindrical container, where the response of the confined granules under axial loading and the load transmission to the contacting structure still remain not fully understood. This paper comparatively studies such a confined compression scenario using a newly developed numerical procedure (Linked DEM-FEM) and a conventional FEM approach. The examined system involved around 7700 polystyrene beads contained in an acrylic thin-walled tube supported at one rim and gagged by two end platens. The compression was applied by displacing one end platen at a constant rate while fixing the other. Characteristics of the compression system, including load-displacement response, force transmission to boundary structure, mobilised bulk wall friction coefficient, and stress distribution on the wall, were evaluated. The majority of the compared physical quantities show reasonable to good agreement, thus giving a convincing quantitative verification for both approaches.