With a low breast cancer incidence and low population density, Greenland is geographically and organisationally challenged in implementing a cost effective breast cancer screening programme where a large proportion of the Greenlandic women will have to travel far to attend. The aim of this paper is to evaluate the cost effectiveness and cost utility of different strategies for implementing population-based breast cancer screening in Greenland. Two strategies were evaluated: Centralised screening in the capital Nuuk and decentralised screening in the five municipal regions of Greenland. A cost effectiveness and cost utility analysis were performed from a societal perspective to estimate the costs per years of life saved and per QALY gained. Two accommodation models for the women's attendance were examined; accommodation in ordinary hotels or in patient hotels. The least costly accommodation model was the hotel model compared with the patient hotel model, regardless of screening strategy. The decentralised strategy was more cost effective compared with the centralised strategy, resulting in 0.5 million DKK per years of life saved (YLS) and 4.1 million DKK per quality-adjusted life year (QALY) gained within the hotel model. These ratios are significantly higher compared with findings from other countries. The sensitivity analysis showed a substantial gap between the most and least favourable model assumptions. The investigated strategies were all estimated to be extremely costly, mostly due to high transportation and accommodation costs and loss of productivity, and none would be accepted as cost-effective per YLS/QALY gained within a conventional threshold level. The least expensive strategy was regional screening with hotel accommodation.