The existence of Mount Merapi in Sleman Regency makes the agricultural land in the area fertile and that becomes the attraction for humans to occupy the region. A high population growth will lead to the residents demand of the availability built-up land higher, that makes the environmental carrying cappacity in Sleman Regency decrease. However, the volcanic activity of Mount Merapi becomes a threat to the people who live in the area of Disaster Prone Areas of Mount Merapi. Predictions on the availability of land as well as the relation to the disaster-prone areas, and the carrying capacity of the environment needs to be done. 2007 - 2017 population data and Landsat 7 ETM + 2007, 2012, and Landsat 8 OLI 2017 imagery will be used in this research as variable in the spatial dynamics model. Meanwhile, physical and accesibility data such as slope, distance from the river, distance from protected area, distance from road, and distance from the center of economic growth will be used as limiting factor of built-up land. Environmental carrying capacity can be observed through a dynamic system model of the relationship between population growth and land availability within the period of 2007 - 2100, then made into the spatial dynamics model to know it's spatial stance. The results of this model show that built-up land increasing every year, packed areas that are suitable for built-up land first, then encroach on areas which not suitable for built-up land and Mount-Merapi Disaster-Prone Areas. © Published under licence by IOP Publishing Ltd.