In this work, a mathematical model is presented for a newly developed cryogenic flow meter which is based on fibre Bragg grating (FBG) principle. The principle of operation is to use the viscous drag force induced by a flowing fluid on an optical fibre placed transverse to the flow. An optical fibre will have a 5 mm long grating element inscribed in it and will be placed so that the sensor is at the centre of the pipe. The fibre will act as the bluff body, while the FBG sensor will pick up the bending strain induced in the fibre due to the drag force. The amount of bending strain which can be measured as a shift in Bragg wavelength can be calibrated to provide the mass flow rate. Here a mathematical model is being presented to predict the operation of the sensor and to calculate the sensor characteristics so that the sensor design can be optimised. The sensor exhibits an exponential relationship between sensitivity and mass flow rate. It is also seen that the sensitivity depends greatly on the fluid properties such as density and viscosity.