Context. Frequencies of acoustic and mixed modes in red giant stars are now determined with high precision thanks to the long continuous observations provided by the NASA's Keplermission. Here we consider the eigenfrequencies of nineteen low-luminosity red giant stars selected in a recent publication for a detailed peak-bagging analysis. Aims: Our objective is to obtain stellar parameters by using individual mode frequencies and spectroscopic information. Methods: We use a forward modelling technique based on a minimization procedure combining the frequencies of the p-modes, the period spacing of the dipolar modes, and the spectroscopic data. Results: Consistent results between the forward modelling technique and values derived from the seismic scaling relations are found but the errors derived using the former technique are lower. The average error for log g is 0.002 dex, compared to 0.011 dex from the frequency of maximum power, νmax, and 0.10 dex from the spectroscopic analysis. Relative errors in the masses and radii are on average 2% and 0.5% respectively, compared to 3% and 2% derived from the scaling relations. No reliable determination of the initial helium abundances and the mixing length parameters could be made. Finally, for our grid of models with given input physics, we found that low-mass stars require higher values of the overshooting parameter.