Plant-based meat analogues are considered a sustainable substitute for meat. However, the current attempts to reproduce the visible fibrous structure on a macro scale (1 mm) have not yet achieved the desired texture properties. The role of the meso-scale fiber structure (50–200 μm) in the meat texture remains uncertain. To characterize the texture properties, this study employed Warner–Bratzler shear force tests and texture profile analysis, comparing cuts that were parallel and perpendicular to the fiber direction. Scanning electron microscopy was employed for the purpose of structural characterization. Anisotropy and texture properties were observed to differ between the meat and the meat analogues. The meat exhibited a fibrous structure at both the macro and meso scales, while the meat analogues displayed a porous structure without a clear fiber direction from the meso scale onward. The texture of meat is primarily determined by the connective tissue and muscle fibers, whereas the texture of meat analogues is mainly influenced by the fibers. This study elucidates the structure–texture relationships of meat and meat analogues at macro and meso scales, developing a mechanistic model to explain their differing responses to mechanical stress. These findings are crucial for improving the texture properties of meat analogues, advancing their ability to mimic meat's texture.