Acoustic manipulation of microparticles and cells, called acoustophoresis, inside microfluidic systems has significant potential in biomedical applications. In particular, using acoustic radiation force to push microscopic objects toward the wall surfaces has an important role in enhancing immunoassays, particle sensors, and recently microrobotics. In this paper, we report a flexural-wave based acoustofluidic system for trapping micron-sized particles and cells at the soft wall boundaries. By exciting a standard microscope glass slide (1 mm thick) at its resonance frequencies <200 kHz, we show the wall-trapping action in sub-millimeter-size rectangular and circular cross-sectional channels. For such low-frequency excitation, the acoustic wavelength can range from 10-150 times the microchannel width, enabling a wide design space for choosing the channel width and position on the substrate. Using the system-level acousto-structural simulations, we confirm the acoustophoretic motion of particles near the walls, which is governed by the competing acoustic radiation and streaming forces. Finally, we investigate the performance of the wall-trapping acoustofluidic setup in attracting the motile cells, such as Chlamydomonas reinhardtii microalgae, toward the soft boundaries. Furthermore, the rotation of microalgae at the sidewalls and trap-escape events under pulsed ultrasound are demonstrated. The flexural-wave driven acoustofluidic system described here provides a biocompatible, versatile, and label-free approach to attract particles and cells toward the soft walls.