A method of manufacturing a semiconductor device is provided, including: forming an oxynitride film having a specific film thickness on a substrate by performing multiple numbers of times a cycle of: forming a specific element-containing layer on the substrate by supplying a source gas containing a specific element into a processing vessel in which the substrate is housed; changing the specific element-containing layer to a nitride layer by supplying a nitrogen-containing gas into the processing vessel; and changing the nitride layer to an oxynitride layer by supplying an oxygen-containing gas and an inert gas into the processing vessel, with this sequence as one cycle, wherein a composition ratio of the oxynitride film having the specific film thickness is controlled by controlling a partial pressure of the oxygen-containing gas in the processing vessel, in changing the nitride layer to the oxynitride layer.