Studies have indicated hazardous consumption of large quantities of alcohol among adults in Lithuania. We assessed the associations of alcohol consumption at baseline with cancer incidence among men in a population-based cohort study, using Cox models adjusted for smoking, education and body mass index. Attained age was used as a time-scale. During follow-up (1978–2008) 1,698 men developed cancer. A higher amount of alcohol consumption (≥140.1 g/week vs. 0.1–10.0 g/week) was positively associated with increased risk of total cancer [hazard ratio (HR) = 1.36, 95 % confidence interval (95 % CI) 1.11, 1.65], upper aerodigestive tract cancer (HR = 2.79, 95 % CI 1.23, 6.34) and alcohol-related cancers (i.e. oral cavity, pharynx, larynx, oesophagus, colorectal and liver cancer) (HR = 1.88, 95 % CI 1.25, 2.85). Compared to occasional drinkers (a few times/year), drinkers 2–7 times/week showed an increased risk of total (HR = 1.45, 95 % CI 1.16, 1.83), alcohol-related (HR = 1.83 95 % CI 1.14, 2.93) and other cancers (HR = 1.35, 95 % CI 1.04, 1.76). Our results showed no statistically significant associations between quantity of alcohol intake per one occasion and risk of cancer. About 13 % of total, 35 % of upper aerodigestive tract, 22 % of alcohol-related and 10 % of other cancer cases were due to alcohol consumption in this cohort of men.