We present theoretical and experimental results on tunneling current in single Fe/MgO/GaAs and double Fe/MgO/GaAs/MgO/Fe tunnel junctions. The charge and spin currents are calculated as a function of external voltage for different sets of parameters characterizing the semiconducting GaAs layer. Transport characteristics of a single Fe/MgO/GaAs junction reveal typical diode as well as spin diode features. The results of numerical calculations are compared with current-voltage characteristics measured experimentally for double tunnel junction structures, and a satisfactory agreement of the theoretical and experimental results has been achieved.