We describe a percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Tissues are considered as structures made of regular healthy, senescent, dead (apoptotic) cells, and studied dynamically, with the ongoing processes including regular cell division to fill vacant sites left by dead cells, healthy cells becoming senescent or dying, and other processes. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. An illustrative application of the developed theoretical modeling approach is reported, confirming recent experimental findings that inhibition of senescence can lead to extended lifespan.