This paper presents closed-form solutions for problems of pressurized holes in anisotropic elastic plates using the complex Stroh formalism. The solutions derived in this paper have broad applications in which the materials are anisotropic elastic materials with up to 21 elastic constants, and the holes can be elliptical and cylindrical. By letting one dimension of the elliptical hole zero, the derived solutions can also be applied to crack problems. The solution can be used as a benchmark for developing numerical methods and is helpful in engineering applications, e.g., interference fit pinned joints with composite materials.