This study uses acknowledged models and which were applicable in international researches to figure up passenger demand elasticity, such as: Double Log, Partial Adjustment Model (PAM) and Cointegration techniques with Error Correction Model. In order to calculate the passenger demand elasticity by bus in the Rio de Janeiro s city from 2004 to 2014 was used Double Log. So as to distinguish short and long run elasticity was employed and compared the results of such models: Partial Adjustment Model (PAM) and Cointegration techniques with Error Correction Model (ECM). This study suggests that the most influential factors of passenger demand by bus in the Rio de Janeiro s city are: gross domestic product, bus fare and number of trips conducted by the fleet. As conclusion, we can claim that there is little distinction in terms of results when compares applied models, except for gross domestic product factor, which presented elastic demand and positive relation using Partial Adjustment Model (PAM) and inelastic demand and positive relation using Error Correction Model (ECM). Bus fare pointed a negative relation for both periods, although an inelastic demand for short run and an elastic demand for long run. Finally, number of trips conducted by the fleet exhibited positive relation and inelastic demand for short and long run.