The asymptote [critical power (CP)] and curvature constant ( W') of the hyperbolic power-duration relationship can predict performance within the severe-intensity exercise domain. However, the extent to which these parameters relate to skeletal muscle morphology is less clear, particularly in endurance-trained individuals, who, relative to their lesser-trained counterparts, possess skeletal muscles that can support high levels of oxygen transport and oxidative capacity, i.e., elevated type I fiber proportion and cross-sectional area (CSA) and capillarity. Fourteen endurance-trained men performed a maximal incremental test to determine peak oxygen uptake (V̇o2peak; 63.2 ± 4.1 ml·min-1·kg-1, mean ± SD) and maximal aerobic power (406 ± 63 W) and three to five constant-load tests to task failure for the determination of CP (303 ± 52 W) and W' (17.0 ± 3.0 kJ). Skeletal muscle biopsies were obtained from the vastus lateralis and analyzed for percent proportion of fiber types, CSA, and indexes of capillarity. CP was positively correlated with the percent proportion ( r = 0.79; P = 0.001) and CSA ( r = 0.73; P = 0.003) of type I fibers, capillary-to-fiber ratio ( r = 0.88; P < 0.001), and capillary contacts around type I fibers ( r = 0.94; P < 0.001) and type II fibers ( r = 0.68; P = 0.008). W' was not correlated with any morphological variables. These data reveal a strong positive association between CP and skeletal muscle capillarity. Our findings support the assertion that CP is an important parameter of aerobic function and offer novel insights into the physiological bases of CP. NEW & NOTEWORTHY This investigation demonstrated very strong positive correlations between critical power and skeletal muscle capillarity, particularly around type I fibers, and type I fiber composition. These correlations were demonstrated in endurance-trained individuals expected to possess well-adapted skeletal muscles, such as high levels of oxygen transport structures and high oxidative capacities, supporting the view that critical power is an important parameter of aerobic function. In contrast, the curvature constant W' was not associated with fiber type composition or capillarity.