The coupling among waveguides on different planes occurs in both transverse and vertical directions. Using the spatial multiwaveguide system, we can interconnect devices in different layers effectively. Based on the weakly coupled-mode theory, the planar waveguide coupling theory is generalized to spatial multiwaveguide system, and the coupled-mode equations of the spatial multiwaveguide system are presented. As an application example, the coupled-mode equation is applied to analyze the coupling properties in spatial three- and four-waveguide systems. The analytical expressions of light intensity distributions and coupling length in the two specific cases are given, and the three-dimensional full-vector beam propagation method is used to verify the analytical results. The analysis result shows that the spatial multiwaveguide system permits uniform and nonuniform power splitting in two orthogonal directions. These analytical formulas are useful in designing three-dimensional directional couplers, which is based on spatial multiwaveguide coupling.