We present 3D, gasdynamic simulations of jet/cloud collisions, with the purpose of modelling the HH 270/110 system. From the models, we obtain predictions of H\(\alpha\) and H\(_2\) 1-0 s(1) emission line maps, which qualitatively reproduce some of the main features of the corresponding observations of HH 110. We find that the model that better reproduces the observed structures corresponds to a jet that was deflected at the surface of the cloud \(\sim 1000\) yr ago, but is now boring a tunnel directly into the cloud. This model removes the apparent contradiction between the jet/cloud collision model and the lack of detection of molecular emission in the crossing region of the HH 270 and HH 110 axes.