High Mountain Asia (HMA) hosts a large number of mountain glaciers, where the terrains are complex and mountain shadows prevail. Solar radiation is an important factor influencing the surface energy balance of glacier and hence glaciers mass balance, as mountain shadows will inevitably decrease the direct solar irradiance on glaciers' surface. Although shadows caused by slope self-shading (SS) have been widely considered in previous research, the influence of topographic shadows (TS) cast by surrounding terrains on solar irradiance on glaciers' surface in HMA still remains unknown. In this study, a topographic solar radiation model was developed, and mountain shadows (including SS and TS) were simulated and validated against manually interpreted and automatically extracted shadows on the basis of Landsat images. Then the influence of TS on solar irradiance on glaciers' surface were evaluated. Results show that, the calculated mountain shadows have a good precision, with a mean mapping accuracy of 0.76, a mean user accuracy of 0.9, and a mean Tanimoto coefficient of 0.74. In HMA, the mean shadow duration over all glaciers is about 1385.5 h per year, accounting for about 30.5% of the daylight time, and exceeding 1900 h for many glaciers, even reaching 3000 h for some glaciers. The average TS shading time over all glaciers is about 719.6 h per year. In Karakoram and Western Tien Shan, the TS shading time is higher than 1000 h per year for many glaciers. For most glaciers, the TS shading time accounts for about one half of the total shading time. The reduction in annual solar irradiance caused by TS exceeds 5.0 W/m2 (3.5% of the annual mean) over 40%, and 7.9 W/m2 (5.7% of the annual mean) over 20% of the glaciers in HMA. On average, the mean ratio of shaded incoming direct solar irradiance caused by TS to the total caused by both TS and SS is about 49.4% over all glaciers. Overall, the solar irradiance reduction is minimal in the interior of the Qinghai-Tibet Plateau, followed by the Himalayas and the Transverse Range, and with the Western Tien Shan and Karakoram being the strongest. In a word, the solar irradiance reduction caused by TS is remarkable, ignoring it could pose a significant impact on the calculation of glacier mass balance in HMA.