Chapter contains a mathematical formulation of the capillary problem. Therefore, the boundary value problem for the Young-Laplace equation in the 3D and axi-symmetric cases is presented and the initial and boundary condition of the 2D meniscus problem are given. The growth angle criterion and some approximated solutions of the 2D meniscus problem are also included. Some analytical and numerical solutions for the meniscus equation in the Cz, EFG and