A one-dimensional photochemical model of the Martian atmosphere has been developed to study variations in the atmospheric composition with solar activity. The low sensitivity of O and CO number densities near the ionospheric peak to solar activity suggests that eddy mixing on Mars is proportional to the solar activity index (K(z) = (F10.7 cm/30) × 1013n-1/2). Due to the higher escape rate and the stronger eddy diffusion at solar maximum the H2 densities above the ionospheric peak are smaller by a factor of 6 than those at the solar minimum. The solar cycle variation of CO+2 by a factor of 2.2 cannot compensate for the variation of H2, and the atomic hydrogen escape flux at solar minimum is larger by a factor of 1.7 than that at solar maximum (the variation of the H number density is a factor of 30). The total hydrogen (H + 2H2) escape flux is stable (though not diffusion limited) and equal to 2.5 × 108 cm-2 sec-1. If eddy diffusion does not depend on solar activity, then the H escape is stable while the total escape flux varies by a factor of 2. The main reason for the hydrogen escape rate being close to the diffusion limit in the early models is that the rate coefficient of the H2 dissociation reaction was larger in the early models by a factor of 3 than the current value. Solar cycle variation of the lower and middle atmosphere is also studied. The CO mixing ratio in the lower and middle atmosphere would vary by a factor of 4 if the species lifetime were a few months. A mechanism of this variation is analyzed. However, since the real lifetime is 6 years the variation is only a factor of 1.35, with a time lag of 2 years.