Material flow analysis is used to quantify the material turnover of a defined system, relying on data about flows and stocks from different sources with varying quality. In this study, the belief that the available data are representative for the value of interest is expressed via fuzzy sets, specifying the possible range of values of the data. A possibilistic framework for data reconciliation in MFA was developed and applied to a case study on wood flows in Austria. The framework consists of a data characterisation and a reconciliation step. Membership functions are defined based on the collected data and data quality assessment. Possible ranges and consistency levels (quantifying the agreement between input data and balance constraints) are determined. The framework allows problematic data and model weaknesses to be identified and can be used to illustrate the trade-off between confidence in the data and the consistency levels of resulting material flows.