This article introduces a new representation of trade preferences termed as the trade distance function, which measures the maximum amount by which import quantities must be deflated or inflated to reach the indifference surface. The properties of this function are discussed and employed to derive systems of inverse demand for imported goods. We illustrate its usefulness by proposing two new parametric forms of trade distance functions. While the trade distance function directly yields Hicksian inverse demand functions of imports, they usually lack closed-form representations in terms of observable variables. This problem, however, need not hinder estimation and could be solved by using the numerical inversion estimation method. Results generally indicate that the suggested modelling and estimation methods are operationally, implying that the trade distance function approach is a promising tool of the empirical analysis of import demands subjected to tight theoretical conditions.