**Objectives:** To investigate mortality among people hospitalised with covid-19 in Switzerland according to epidemic wave, age, sex, comorbid conditions and intensive care unit (ICU) occupancy. **Design:** Population-based, national study. **Setting:** Mandatory surveillance reports from all hospitals in Switzerland. **Participants:** All 22,648 people who tested positive for SARS-CoV-2 infection and were hospitalised between February 24, 2020 and March 01, 2021 in Switzerland with complete information about age, sex, and comorbidities. **Main outcome measures:** Survival after positive SARS-CoV-2 test among people hospitalised with covid-19 by epidemic wave, age, sex, comorbid conditions and ICU occupancy, expressed as adjusted hazard ratios (aHR) of death and probability of survival over time and at 40 days, all with 95% credible intervals (CrI). **Results:** Of 22,648 people hospitalised with covid-19, 4,785 (21.1%) died. Bayesian survival models adjusted for age, sex, and the presence of comorbidity showed that survival was lower during the first epidemic wave than the second (standardised predicted survival probability at 40 days 76.1% versus 80.5%; aHR of death 1.38, 95% CrI 1.28 to 1.48). During the second epidemic wave, occupancy among all available ICU beds (certified beds and add-on beds) in Switzerland varied between 51.7% and 78.8%. Modelling the association between survival and ICU occupancy with restricted cubic splines indicated stable survival when ICU occupancy was below 70%, but worse survival when ICU occupancy exceeded 70%. This threshold of 70% occupancy among total available ICU beds corresponded to around 85% occupancy among certified beds. Survival was decreased for men, older people, and patients with comorbid conditions. Comorbid conditions reduced survival more in younger people than in older people. As single comorbid condition, hypertension was not associated with poorer survival, but appeared to increase the risk of death in combination with a cardiovascular disease. **Conclusion:** Survival after hospitalisation with covid-19 has improved over time, consistent with improved management of severe covid-19. The decreased survival starting at approximately 70% ICU occupancy in Switzerland supports the need to introduce measures for prevention and control of SARS-CoV-2 transmission in the population far before ICUs are full.