Maps from before the Chubb Hill Road and the Whitby-Loftus railway was built show Arundel Beck running along a valley called Arundel Hole. It starts from a spring near Rose Avenue (NZ 8884 1123) - now underground - and runs underground under the old railway line passing under Stakesby Road just east of the site of the railway bridge.
It runs behind almost exactly under the car park and access road to Spring Vale Medical Centre and under Rievaux Road. It meets Chubb Hill Road at The Circle and runs under Chubb Hill Road where it can be heard running under manhole covers in the road. It continues until it joins Stakesby Beck at the end of Arundel Place. It then flows to the harbour as Bagdale Beck.