Herbig-Haro (HH) objects, which are observed in molecular, ionic and atomic line emission, are shocked regions within outflows associated with low mass star formation. A 1-D, planar shock code, MHD_VODE, which incorporates an extensive chemistry and calculates the population distributions of various important species throughout the shock wave, is used to model the H(_2) , [Fe II and [C I] line intensities observed from 14 HH objects. It is found that models of non-equilibrium J-type shocks with magnetic precursors are required to reproduce the observed H(_2) emission. These models have shock velocities in the range of 30-50 km s(^-) pre-shock densities of typically 10(^4) cm(^-3) and ages of the order of a few hundred years. However, such models predict a low electron density and are not able to reproduce the observed [Fe I I ] and [C I] emission. The ionization of H following dissociation of H (_2) in a J-type shock results in weak H(_2) emission but can produce the ionization fraction required for the atomic and ionic forbidden line emission. Thus, an elementary representation of a bow shock, consisting of a J-type shock with a magnetic precursor and a J-type shock, respectively, proves successful in reproducing both the H(_2) and Fe I I ] emission. I t is necessary to assume that Fe has previously been eroded from dust grains, probably by the earlier passage of a C-type shock wave. These findings are consistent with observations, which have suggested that HH outflows are episodic phenomena and that the emission from HH objects arises in bow shocks.