The lateral tidal open boundary conditions which force tides of internal regions are estimated by an adjoint data assimilation system which combines observed coastal tidal water level data into a hydrodynamic model for the East Coast of the United States. In this system, the two-dimensional Princeton Ocean Model (POM ) with an orthogonal curvilinear grid system is used as a forward model. Control variables are the harmonic constants (amplitude and phase) of tidal constituents (M2,S2,K1,O1,N2, K2) along the open boundary. The cost function is defined by the water level misfits between the observed data and model-simulated results. The limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method for large-scale optimization is implemented to minimize the cost function. Identical twin experiments with model-generated pseudo-observations are performed to verify the data assimilation system. The results from the twin experiments show that the true solution of the control variable can be recovered by assimilating pseudo-observations at tidal stations into the model. The actual predicted tidal elevations at selected tidal stations along the East Coast are assimilated to obtain the optimal tidal open boundary conditions. The results show that the model-simulated tidal elevations forced by the optimal open boundary conditions are more accurate than model results forced by the open boundary conditions derived from Schwiderski's global tidal model. For the M2 constituent, the maximum RMS error with data assimilation is 14 cm and the minimum correlation coefficient is 0.96. For the 9 coastal stations, the RMS errors are less than 5 cm. The results from the experiment in which the 5 tidal constituents are considered together show that the RMS errors at the 9 coastal stations are less than 7 cm, and the correlation coefficients between tidal prediction and model results are greater than 0.99.