Space charge limited (SCL) transport in solids involves high charge injections in which the amount of the charges injected into the solids is much larger than the thermal or intrinsic concentration of the solids. A two-dimensional (2D) analytical model of the space charge limited current (SCL) injection in a trap-free and a trap-limited solid will be developed. For a trap-limited solid, traps with exponentially distributed in energy is emphasized and studied. By considering the electrons are injected from an infinitely long emission strip of width W, the one-dimensional (1D) SCL current density is enhanced by a factor of 1+F X(4/phi)/(W/L), where F = 1/(l+2) measures the mean position of the injected electrons in a solid of length L, and l is the ratio of the distribution of the traps to the free carriers. The analytical formula is verified by using a 2D device simulator (Medici).