The volume and freshwater transports through the Canadian Arctic Archipelago (CAA) are assessed using the unstructured-mesh Finite-Element Sea-ice Ocean circulation Model (FESOM) in a global setup with the CAA resolved at the 5 km scale. The hindcast simulation realistically represents fluxes through the main gates of the Arctic Ocean and the Arctic sea ice conditions. During the period 1968-2007 the mean volume transports through Lancaster Sound and Nares Strait amount to 0.86 Sv and 0.91 Sv, respectively. The monthly mean volume transport through western Lancaster Sound is highly correlated with the observational estimate (r=0.81). The seasonal variability of the Lancaster Sound transport is well represented in the model. The simulated mean CAA freshwater export rate is 123 mSv, slightly higher than the observational estimate. The interannual variability of CAA volume transports is determined by sea surface height (SSH) gradients between the Arctic Ocean and northern Baffin Bay. The sea level upstream of Lancaster Sound is mainly determined by that along the Beaufort Sea coast, which can be explained by changes in the wind regimes (cyclonic vs. anticyclonic) associated with release or accumulation of freshwater in the Beaufort Gyre. Sea level variations downstream of Lancaster Sound and Nares Strait are connected to SSH variations in the eastern Baffin Bay and in the Labrador Sea, which can be attributed to the variability of ocean-atmosphere heat fluxes. Both processes upstream and downstream of the CAA are linked with the North Atlantic Oscillation type of atmospheric variability. The local mesh refinement of ~5 km allows us to investigate the contribution of individual narrow straits to the Parry Channel volume transport. The volume transports through these straits show a very similar variability.