Four major potato varieties in western Hubei namely Marco, Huashu 12 (h12), Huashu 16 (h16), and Eshu 10 (e10) were steamed to investigate the relationships between the texture and stress relaxation properties of steamed potatoes and the chemical components, water distribution, and starch properties of raw potatoes. It turned out that h16 showed higher hardness, elasticity and cohesiveness. Its chewiness, stickiness and adhesiveness were significantly different from those of other varieties. The hardness of Marco was significantly lower than that of the other three varieties. Adhesiveness and hardness significantly varied among Marco, h12 and e10, while other TPA parameters did not. Stress relaxation analysis showed that the equilibrium elastic coefficient, attenuation elastic coefficient and damping coefficient of Marco were significantly higher than those of the other varieties, while its relaxation time was intermediate. The contents of starch, protein, free amino acids, total soluble sugar, and reducing sugar in raw potatoes were determined to be 9.17%–14.96%, 1.73%–3.30%, 136.43–240.68 mg/g, 6.12%–12.00%, and 0.14%–0.30%, respectively. After steaming, the contents of protein and free amino acids decreased, whereas those of soluble sugar and reducing sugar increased. Correlation analysis revealed that the higher the starch content of raw potatoes, the lower the hardness after steaming. In contrast, the hardness increased with increasing amylose content, starch crystallinity, and gelatinization enthalpy. In addition, higher protein content led to stronger chewiness, cohesiveness, and adhesiveness. The chemical composition also influenced the water distribution in steamed potatoes. A higher proportion of bound water was associated with higher adhesiveness and a shorter relaxation time. Aspartic acid, glutamic acid, and proline, as well as arabinose, mannose, glucuronic acid, glucose, and galactose were identified as key components regulating the texture and stress relaxation characteristics of steamed potatoes. These results provide guidance for the texture control of steamed potatoes.