The process of sedimentation that occurred in the river can cause siltation of the river resulting in overflow of water to the surface or flooding. This siltation is caused by sedimentation. In this paper we consider sedimentation problem occured at the confluence of two rivers. We therefore develop a mathematical model of the problem and solving the model by using Meshless Local Petrov-Galerkin (MLPG) method. This MLPG method is an alternative way to solve this problem because it does not require mesh or grid. It therefore is very helpful in minimizing both running time of the numerical calculation and computer memory. From the results of numerical simulation we obtain that for the flow of the bend stream, there exists a decreasing in the height of the sediment is around 0002 and an increasing in speed of about 0.000848 during the initial velocity v = 0.1. When the initial velocity v increases, it will also increase in the speed and decrease in the height of the sediment. It can be occured when we put v = 0.9, an increasing in water depth of about 0.015832, increasing in speed of around 0.068586, and the height of the sediment decrease by approximately 0.166470. The both speed and depth affect the height of the sediment on the riverbed. Likewise, the height of the straight stream sediment increases about 2.792678, the speed decreases about 5.172373, the depth of the river is also down about 2.792678, when the first river debit and the second river debit are Q=0.5. If we put the first river and the second river are different, when the first river debit is 0.3 and 0.9 for the second river debit, sediment remained ride height is about 0.297025, the speed of the river downs about 1.651025 and the depth of the river decreases approximately 0.278835.