Ferroelectric (Ba, Sr) TiO$_3$(BST) thin films have attracted much attention for use in new capacitor materials of dynamic random access memories (DRAMs). In order to apply BST to the DRAMs, the etching process for BST thin film with high etch rate and vertical profile must be developed. However, the former studies have the problem of low etch rate. In this study, in order to increase the etch rate, BST thin films were etched with a magnetically enhanced inductively coupled plasma(MEICP) that have much higher plasma density than RIE (reactive ion etching) and ICP (inductively coupled plasma). Experiment was done by varying the etching parameters such as CF$_4$/(CF$_4$+Ar) gas mixing ratio, rf power, dc bias voltage and chamber pressure. The maximum etch rate of the BST films was 170nm/min under CF$_4$/CF$_4$+Ar) of 0.1, 600 W/-350 V and 5 mTorr. The selectivities of BST to Pt and PR were 0.6 and 0.7, respectively. Chemical reaction and residue of the etched surface were investigated with X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectroscopy (SIMS).