Aim The present cross‐sectional study aimed at assessing muscle strength of hands, the dominant arm and legs in Spanish institutionalized elderly people according to sex, age and cognitive status. Methods A total of 153 elderly subjects (102 females, 51 males, mean age 83.6 ± 6.8 years) living in the region of Madrid were measured for handgrip strength (kg) with a Takei TKK 5101 digital dynamometer (range 5–100 kg, precision 0.1 kg), and arm and leg endurance strength (repetitions) according to the Rikli and Jones tests. Cognitive status was determined with the Mini‐Mental State Examination (MMSE). Results The values for men and women were, respectively: 23.5 ± 7.3 kg and 11.6 ± 4.6 kg (right handgrip), 22.0 ± 7.8 kg and 10.7 ± 4.8 kg (left handgrip), 13 ± 5 and 10 ± 5 repetitions (arm strength), 8 ± 5 and 5 ± 4 repetitions (legs strength), and 21 ± 6 and 17 ± 7 (MMSE score). All parameters were significantly higher for men (P ≤ 0.01), but strength decline with age was less pronounced in women. In all MMSE groups, lower strength was associated with lower cognitive status. Conclusions Strength values were lower in older subjects in both sexes; this difference was higher in men than in women. Higher strength values were associated with better cognitive status, which was the most influencing variable, even more than sex and age. Geriatr Gerontol Int 2013; ●●: ●●–●●.