The similarity law was not always valid because of the occurrence of the forbidden processes (e.g. stepwise ionization, charge exchange) for which the similarity law might be violated. In order to exam the validity of the similarity relations of low pressure glow discharge, a fluid model of gas discharge was established with the forbidden processes. The dimension ratio of the gap A and B was set at 2:1, the pressures for the gap A and B were 60Pa and 120Pa, respectively. The discharge parameters (such as electric potential, electric field, space charge density, electron density and ion density) in two geometrical similar gaps were comprehensively investigated. The simulation results indicated that the discharge was identified as a typical glow discharge. The impact of the forbidden processes caused small deviations, but was not significant in our case. The physical parameter relations of the two similar gaps were found to be in agreement with the theoretical ones derived by the similarity law.