Agricultural robotics has emerged as a research area within robotics, with a particular focus on designing end effectors that are adapted to the physical characteristics of the target fruits. Acquiring a comprehensive understanding of the physical and mechanical properties specific to tomato fruits not only minimizes mechanical damage during grasping processes but also serves as a foundation for the optimal design of gripping components. In this study, the Syngenta Sibede variety of tomatoes was used as the experimental material. The reversible viscoelastic behavior and deformation characteristics of tomato fruits were approximated using a four-element Burgers model through creep testing. The fitting coefficients for the model exceeded 0.99. The creep parameters for the four ripening stages of tomatoes were obtained, and the correlation between the ripening stage, deformation value, and creep parameters was analyzed. Correlation analysis was performed to examine the relationships between each parameter and creep deformation, revealing significant and highly significant correlations. Inter-parameter correlations were also found to be highly significant. Puncture tests were conducted on tomatoes. The exocarp rupture force of the green-ripening stage was 9.224 ± 0.901 N, which was 53.87%, 70.63%, and 104.01% higher than that of the semi-ripening stage, early firm-ripening stage, and mid-late firm-ripening stage, respectively. This study suggests that when harvesting tomatoes at the semi-ripening stage and beyond, attention should be paid to trimming the stem. Compression experiments were conducted on tomatoes, and it was discovered that under the same ripening stage, the axial compressive rupture force of tomatoes was greater than the radial rupture force. Tomatoes exhibited anisotropic behavior. The grasping direction is axial, which can be used as the new design direction of the end-effector.