In this paper high-order triangular elements are implemented in the framework of the Arbitrary Lagrangian-Eulerian method for the analysis of large strain coupled consolidation problems in geomechanics. The theory of coupled consolidation, as well as details of the high-order elements, including quadratic (6-noded), cubic (10-noded), quartic (15-noded) and quantic (21-noded) elements, are discussed. The accuracy and the efficiency of high-order elements in the analysis of undrained problems are presented by solving two classical geomechanics problems. These include the bearing capacity of soil under a footing and the large deformation analysis of a vertical cut subjected to a surcharge loading. Based on the numerical results, it is shown that high-order elements not only improve the accuracy of the solution, but can also significantly decrease the required computational time.