In this work we address the problem of dealing with data inconsistencies while integrating data sets derived from multiple autonomous relational databases. The fundamental assumption in the classical relational model is that data is consistent and hence no support is provided for dealing with inconsistent data. Due to this limitation of the classical relational model, the semantics for detecting, representing, and manipulating inconsistent data have to be explicitly encoded in the applications by the application developer. In this paper, we propose the flexible relational model, which extends the classical relational model by providing support for inconsistent data. We present a flexible relation algebra, which provides semantics for database operations in the presence of potentially inconsistent data. Finally, we discuss issues raised for query optimization when the data may be inconsistent.>