Photometric observations from the last decade have revealed additional low-amplitude periodicities in many classical pulsators that are likely due to pulsations in non-radial modes. One group of multimode RR Lyrae stars, the so-called 0.61 stars, is particularly interesting. In these stars, the radial first overtone is accompanied by additional signals with period ratios around 0.61. The most promising explanation for these signals is pulsation in non-radial modes of degrees 8 and 9. If the theory behind the additional signals in the 0.61 stars is substantiated, it would allow us to use non-radial modes to study classical pulsators. We aim to perform asteroseismic modelling of selected 0.61 stars with independently determined physical parameters to test whether this assumption behind the modelling leads to correct results. Namely, we test whether the additional signals are indeed due to non-radial modes of the proposed moderate degrees. We selected a number of RR Lyrae stars that are also 0.61 stars and have good observational constraints on their other physical parameters. We assume that the nature of those modes is correctly explained with non-radial modes of degrees 8 or 9. Using this assumption and observational constraints on physical parameters, we performed asteroseismic modelling to test whether the observed periods and period ratios can be reproduced. For the majority of selected targets, we obtained a good match between observed and calculated periods and period ratios. For a few targets however, the results obtained are ambiguous and not straightforward to interpret.