Geomagnetically induced currents (GICs) are a well-known terrestrial space weather hazard. They occur in power transmission networks and are known to have adverse effects in both high and mid-latitude countries. Here, we study GICs in the Irish power transmission network (geomagnetic latitude 54.7--58.5$^{circ}$ N) during five geomagnetic storms (06-07 March 2016, 20-21 December 2015, 17-18 March 2015, 29-31 October 2003 and 13-14 March 1989). We simulate electric fields using a plane wave method together with two ground resistivity models, one of which is derived from magnetotelluric measurements (MT model). We then calculate GICs in the 220, 275 and 400~kV transmission network. During the largest of the storm periods studied, the peak electric field was calculated to be as large as 3.8~V~kmtextsuperscript{-1}, with associated GICs of up to 23~A using our MT model. Using our homogenous resistivity model, those peak values were 1.46~V~kmtextsuperscript{-1} and 25.8~A. We find that three 400 and 275~kV substations are the most likely locations for the Irish transformers to experience large GICs.