In normal somatic cells, telomere length shortens with each cell replication. This progressive shortening is associated with cellular senescence and apoptosis. Germ cells, stem cells, and the majority of cancer cells express telomerase, an enzyme that extends telomere length and, when expressed at sufficient levels, can immortalize or extend the life span of a cell line. It is believed that telomeres switch between two states: capped and uncapped. The telomere state determines its accessibility to telomerase and also the onset of senescence. One hypothesis is that the t loop, a large lariat-like structure, represents the capped state. In this paper we model a telomere state on the basis of the biophysics of t-loop formation, allowing us to develop a single mathematical model that accounts for two processes: telomere length regulation for telomerase positive cells and cellular senescence in somatic cells. The model predicts the steady-state length distribution for telomerase positive cells, describes the time evolution of telomere length, and computes the life span of a cell line on the basis of the levels of TRF2 and telomerase expression. The model reproduces a wide range of experimental behavior and fits data from immortal cell lines (HeLa S3 and 293T) and somatic cells (human diploid fibroblasts) well. We conclude that the t loop as the capped state is a quantitatively reasonable model of telomere length regulation and cellular senescence.