Observations revealed that various kinds of oscillations are excited in solar flare regions. Quasi-periodic pulsations (QPPs) in the flare emissions are commonly observed in a wide range of wavelengths. Recent observations have found that fast-mode magnetohydrodynamic (MHD) waves are quasi-periodically emitted from some flaring sites (quasi-periodic propagating fast-mode magnetoacoustic waves; QPFs). Both of QPPs and QPFs imply a cyclic disturbance originating from the flaring sites. However, the physical mechanisms remain puzzling. By performing a set of two-dimensional MHD simulations of a solar flare, we discovered the local oscillation above the loops filled with evaporated plasma (above-the-loop-top region) and the generation of QPFs from such oscillating regions. Unlike all previous models for QPFs, our model includes essential physics for solar flares, such as magnetic reconnection, heat conduction, and chromospheric evaporation. We revealed that QPFs can be spontaneously excited by the above-the-loop-top oscillation. It was found that this oscillation is controlled by the backflow of the reconnection outflow. The new model revealed that flare loops and the above-the-loop-top region are full of shocks and waves, which is different from the previous expectations based on a standard flare model and previous simulations. In this paper, we will show the QPF generation process based on our new picture of flare loops and will briefly discuss a possible relationship between QPFs and QPPs. Our findings will change the current view of solar flares to a new view in which they are a very dynamic phenomenon with full of shocks and waves.