Muscle strength is highly heritable and predictive for multiple adverse health outcomes including mortality. Here, we present a rare protein-coding variant association study in 340,319 individuals for hand grip strength, a proxy measure of muscle strength. We show that the exome-wide burden of rare protein-truncating and damaging missense variants is associated with a reduction in hand grip strength. We identify six significant hand grip strength genes,KDM5B,OBSCN,GIGYF1,TTN,RB1CC1, andEIF3J. In the example of the titin (TTN)locus we demonstrate a convergence of rare with common variant association signals and uncover genetic relationships between reduced hand grip strength and disease. Finally, we identify shared mechanisms between brain and muscle function and uncover additive effects between rare and common genetic variation on muscle strength.