The electronic states of fullerene structures are modulated by external environments, such as magnetic fields, electric fields, and stress, which exhibit unique physical properties. Compression, i.e., the application of compressive stress to fullerene structures, plays an important role in modulating the optoelectronic properties of fullerene materials. Herein, we comprehensively investigate the stability, band structures, Bloch wave functions, and optical responses of two-dimensional quasi-tetragonal phase C-60 (qTP C-60) and quasi-hexagonal phase C-60 (qHP C-60) under external stress. The findings reveal that qTP C-60 and qHP C-60 can be stabilized within a certain range based on the regulation of external stress. This kind of stress can considerably alter the band structures of qTP C-60 and qHP C-60, thereby changing the positions of the highest occupied and lowest unoccupied molecular orbitals. The analysis of Bloch wave functions can help visualize the electronic density distribution of qTP C-60 and qHP C-60 structures, indicating a considerable influence of stress on the electronic state distribution of the system. This influence results in changes in the band structure, thus affecting the electronic distribution state and optical response. Furthermore, qTP C-60 and qHP C-60 exhibit surface plasmon effects within a specific wavelength range, suggesting their potential applications in optoelectronic devices.