In this dissertation, the theory of jet is employed to present an analytical model for calculating maximum scour depth under pressure flow conditions below bridge deck in submerged regime. This thesis is generally divided into two parts. In the first part, an analytical model is developed by considering only the blockage created by the bridge deck (without bridge pier). The analytical model proposed by Hoffmans (2009) for a stationary fluid volume is extended to include the running flow unserneath the bridge deck. The flow underneath the deck was simulated as a jet flow, and the velocities in the shear stress equation were calculated using near-bed jet velocity equation. Substituting the velocity into the shear stress equation and including the forces in the control volume, the momentum momentum was applied along the vertical direction. Using the existing experimental data and comparing bed shear stress and critical shear stresses, an equation was obtained for the correction factor appeared in the momentum equation. By back substituting this factor into the equation of momentum, a polynomial equation was obtained for calculating the maximum scour depth. In the second part, the effect of the presence of bridge pier on pressure flow scour was investigated. Considering the effect of the pier on the flow within the scour hole and upstream flow, equations were developed to calculate mean velocity under the deck. Jet flow was considered for two cases; developing and and fully developed flow regions. For each case, two different equations were obtained to calculate the near-bed velocity. The equation of momentum was applied and two separate equations were obtained for calculating the maximum scour depth. The procedure for calculating coefficients of the equations was the same as that followed in the first part. In the second approach, the entire flow beneath the deck was taken as a downward flow, with the equation of momentum written for the zone beneath the deck. Experimental data was used to calculate the friction coefficients in the shear stress equation. Finally, the obtained results from the presented equations were compared against experimental data. In the pressure flow scour of the deck, 66% of the calculated results fell within -33% to +55% of error with reference to the experimental data. When pressure flow scour of the pier was concerned, 52% and 55% of the results fell within the same range of error in fully developed flow and developing flow, respectively. The results obtained from the three cases (deck scour and pier scour of developing flow and fully developed flow) generally exhibited the same trends in terms of Froude number and deck distancee to original bed as those of experimental data. In the second approach (pressure flow scour of the bridge pier), the develoed relationship for scour depth was evaluated as inappropriate due to inconsistency of the obtained results with the experimental values of friction coefficient. Keywords: Pressure flow scour, Submerged regime, Jet flow, Deck submergence, Bridge pier, Equation of momentum.