In this study, the flagellar motility of a swimmer microorganism as a model of a human sperm cell, inside a two-dimensional channel as a model of the female reproductive tract containing a viscous fluid, is numerically investigated. The Navier–Stokes equations governing the fluid are coupled with the equations governing the models flagellum via applying a fluid–solid interaction approach and then solved using the finite element method. To stimulate the flagellum to move, a prescribed sinusoidal waveform is applied to it. The strain induced by this waveform along the flagellum initiates a continuous interaction between the flagellum and the fluid. The simulations are validated using data available in the literature. A very good agreement is seen between them. The results show that by decreasing the Young modulus of the flagellum as well as increasing the fluid viscosity, the swimming velocity of the model significantly decreases. It is found that for lower Young modulus of the flagellum, the effect of the fluid viscosity on the flagellar deformation is stronger. It is also found that for higher amplitude of the waveform applied to stimulate the flagellum, both the swimming velocity of the model and the average work rate are greater. Moreover, it is found that in a channel with a smaller height, the model swims at a higher speed and with a higher average work rate.