Unbounded domain problems are frequently encountered in geotechnical engineering and infinite elements are often used effectively for simulation. The weak form quadrature element method is an effective numerical tool in which the computational accuracy is often improved through increasing the order of integration. An infinite weak form quadrature element is developed and applied to the analysis of unbounded domain problems in geotechnical engineering. Based on coordinate transformation, an unbounded domain is mapped onto a standard region where numerical integration and numerical differentiation are conducted and the conventional numerical integration points and weights in the weak form quadrature element method are retained. Numerical examples in the areas of transient seepage, consolidation and elastostatic analysis are given and the results are compared with analytical solutions or those of other numerical methods. It is shown that the infinite weak form quadrature element is simple and applicable to solution of various unbounded domain problems, while conventional elements are used during discretization of the domain of interest. In addition, the dependence on the pole of coordinate transformation can be alleviated considerably with the increase of the integration order of the element. Consequently, computational resources are reduced significantly and accuracy of results is enhanced.