Analytical solutions for space charge limited currents in collisionless, electron-free sheaths are given for Cartesian, spherical, and cylindrical geometries. Constant current and current density are assumed. Until now, the problem of space charge limited current has not been solved either directly, in terms of series expansions, or numerically, for spherical and cylindrical objects. Analytical results show that the geometry of the system is important for determining the space charge limited current, sheath thickness, and sheath potential profile. This solution method can be used to solve similar nonlinear differential equations. (c) 2006 American Institute of Physics.