The non-thermal electrons accelerated during solar flares can produce enhanced and broadened chromospheric lines when they precipitate into the chromosphere. In this paper, we propose a method to diagnose the non-thermal processes using two chromospheric lines, ${H\alpha}$ and Ca ${\sc ii} 8542 \AA}$ lines. First, we perform non-LTE calculations of these two lines for various (thermal) model atmospheres and (non-thermal) electron beams. Since the two lines have different sensitivities to the non-thermal electrons, a set of line spectra can uniquely determine a model atmosphere and an electron beam. We then apply this method to a solar flare for which we have observed two-dimensional spectra of the two lines. In particular, we examine the temporal variation of thermal vs. non-thermal effects in flare bright kernels, as well as the spatial variation across flare ribbons. The results show clearly that the non-thermal effects appear most obviously at the flare maximum, and preferentially at the outer edges of flare ribbons. The results are consistent with flare theoretical models.