In this study, the Burger model combining the Maxwell and Voight–Kelvin model units as well as modified mechanical models were employed to analyze the shear creep mechanism of wood. Off-axis compression tests were conducted on Japanese cypress specimens, and a mechanical analysis of the shear creep mechanism was performed. First, the measured creep compliance curves [JTL(t)] were fitted using the Burger model, which is a typical model that explains the creep behavior of wood. Furthermore, three modified Burger models with non-Newtonian dashpots were proposed to explain the measured data more accurately: model 1 — only the dashpot in the permanent strain unit is non-Newtonian; model 2 — both dashpots are non-Newtonian; and model 3 — only the dashpot in the delayed elastic strain unit is non-Newtonian. The results showed that the average values of the coefficients of determination of the Burger model and models 1, 2, and 3 were 0.940±0.061, 0.979±0.034, 0.978±0.024, and 0.889±0.132, respectively. The number of specimens that could be fitted with a tolerance error of 0.1% was 43 out of 50 with the Burger model, 45 with model 1, 25 with model 2, and 45 with model 3. However, the Burger model exhibited large discrepancies between the theoretical and measured values, model 2 could not be used to explain several specimens, and model 3 exhibited a delayed elastic strain behavior that was inconsistent with the definition. Therefore, we conclude that model 1 is the most appropriate for studying the shear creep behavior of wood.