This paper examines the use of neural network to model nonlinear tsunami processes for forecasting of coastal waveforms and runup. The three‐layer network utilizes a radial basis function in the hidden, middle layer for nonlinear transformation of input waveforms near the tsunami source. Events based on the 2006 Kuril Islands tsunami demonstrate the implementation and capability of the network. Division of the Kamchatka‐Kuril subduction zone into a number of subfaults facilitates development of a representative tsunami dataset using a nonlinear long‐wave model. The computed waveforms near the tsunami source serve as the input and the far‐field waveforms and runup provide the target output for training of the network through a back‐propagation algorithm. The trained network reproduces the resonance of tsunami waves and the topography‐dominated runup patterns at Hawaii's coastlines from input water‐level data off the Aleutian Islands.