Soft magnetic thin films with in-plane uniaxial magnetic anisotropy are of significant importance for a broad range of technological applications, including high-frequency power conversion. In-plane uniaxial anisotropy in amorphous films is of particular interest for ultra-low materials loss and MHz frequency operations. The present work is focused on one of the fundamental mechanisms, i.e., residual stress, that can negate the uniaxial anisotropy in amorphous films by engendering perpendicular magnetisation and hence, undermining the soft magnetic performance. It is quantified how the nature of residual stress, compressive or tensile, transforms the magnetisation from an in-plane to an out-of-plane configuration, also well-known as spin-reorientation transition (SRT). A correlation between engineered residual stress in multilayer stacks, induced by the uneven expansion of metallic/dielectric layers following a thermal-shock scheme, and SRT mechanism demonstrates tensile stress inside the films undermines the soft magnetic performance. We suggest the magnetic softness can be retained by eluding sources of tensile stress during fabrication or post-processing of the amorphous films.