A mass flow sensor based on the frequency shift of a resonating microstructure is being developed, using a measurement principle of the thermoanemometry type. The sensor is to be applied for mass flows up to 10 standard cubic centimeters per minute (sccm; 10sccm = 0.17 mg s-1), with a high sensitivity, a high resolution and a fast response. Here we report on the first prototype consisting of a 2 μm thick membrane: the temperature elevation of the thermally excited vibrating membrane affects its resonance frequency. The three-dimemsional heat transfer within the membrane and the mass flow is modeled, and expressions are derived for the resonance frequencies of initially curved and stressed membranes. Experiments have been carried out for nitrogen flows of up to 500 sccm passing over thermally excited membranes. Predicted and measured values for the shift of the resonance frequency agree well. The sensitivity of the average temperature elevation to the mass flow is quite small: at 10 sccm the cooling effect of the mass flow is only 0.2% of the heat loss by conduction to the substrate. At a resonance frequency of 5.0 kHz, and an average temperature elevation of the mebrane of 8°C, this still leads to a frequency change of 13 Hz in the mass flow range from zero to 10 sccm. Suggestions are presented for increasing the sensitivity of the sensor.