The aim of this study is to present the solutions for the near-field tsunami amplitudes caused by submarine landslumps and slides spreading in two orthogonal directions. A linearized shallow water wave theory is derived. The transform techniques (Fourier and Laplace transform) are used for the solution of Laplace equation. The results show that if the ratio of the velocties is v(1)/v(2)=0.1, the numerical results are almost the same as the values obtained for one dimensional movement of the slumps and slides. But. when the ratio of the velocties is v(1)/v(2)= 1, obtained normalized peak amplitudes, eta(max)/zeta(0) are smaller than the numerical values for one dimensional solution. It is concluded that normalized peak amplitudes for the models are small because of the interaction of the velocities. Numerical examples are presented for various parameters. (c) 2005 Elsevier Ltd. All rights reserved.