Minimal surfaces are widely exist in nature which is an important type of surface with zero mean curvature. Different methods can be adopted to solve because of its many consistent mathematical structures. Minimal surface can be defined as the critical point of the area functional.Therefore it can be expressed by the variational equations or the equivalent Lagrangian-Eulerian equations. The latter is also known as second order elliptic equations. Then the analytical or approximate solutions can be obtained through differential equations and approximate solutions through variational equations. Minimal mapping is a special mapping between two Riemannian manifolds, however Weierstrass presented a general solution of the equation of minimal surfaces from another point of view without area concept. With Weierstrass representation for minimal surface, various kinds of excellent minimal graphes can appear on the computer, which are hard to image before they model because of the complexity in the topology and the elusive symmetry on the geometry. Best immersion Boy's surface graphes in 3D Euclindean space are drawn, Moreover, several kinds of architectual modeling with minimal surfaces or harmonic surfaces are discussed.