Metasurfaces, treated as equivalent two-dimensional (2D) metamaterials, have the advantages of compactness and simplicity. In spite of the recent related booming researches, the non-perforated or surface-bonded ultrathin elastic metasurfaces have seldom been reported, since there exists a big challenge in designing such a single unit to satisfy the requirements of 2π phase span and simultaneous high transmission. In this paper, an elastic meta-structural functional unit is carefully designed, enabling an effective wave manipulation application for Structural Health Monitoring (SHM) and Non-destructive Evaluation (NDE) communities. Through conducting a series of parametric studies, the full 2π phase span and high transmittance can be achieved by a singl-elayer meta-structural unit. When proceeding to calculate the phase profile for realizing the full 2π phase span, the height of the unit cell stub is tuned by exploring a finite element model (FEM) using harmonic analysis. The nephograms of the phase shift varying with the stub height and excitation frequency exhibit the successful achievement of a full 2π span covering a wide frequency range. Further, to enable a high transmittance at the same time, two sets of parametric studies are complementally carried out through adjusting two additional structural parameters. Subsequently, various single-layer elastic meta-structures are designed with the proposed unit cell for the peculiar transmission manipulation of antisymmetric Lamb waves demonstrated by numerical simulations. The paper finishes with summary, concluding remarks, and suggestions for future work.