Tsunami waves are usually modeled using the 2-D shallow water equations. These equations can only be solved numerically, and have little analytical use. However, many communities live at the end of narrow bays. In such bays the problem can be simplified to one dimension, by making a few physical assumptions. The resulting equations are then solved analytically for flat-sloping and piecewise sloping U-shaped bays. These results are compared to 2-D numerical models to understand the validity and limitations of our assumptions. Future application of this work may be in real time tsunami prediction for bay communities.