The spatial Durbin model (SDM) is one of the most widely used models in spatial econometrics. It originated as a generalisation of the spatial error model (SEM) under a non-linear parametric restriction (see Anselin (1988, pp. 110–111)). This restriction should be tested to select an appropriate model between SDM and SEM. Perhaps, due to the complexity of executing a test for a non-linear hypothesis, this restriction is rarely tested in practice, though see Burridge (1981), Mur and Angulo (2006) and LeSage and Pace (2009, p. 164). This paper considers an alternative linear hypothesis to test the suitability of the SDM. To achieve this, we first use Rao’s score (RS) testing principle and then Bera and Yoon (1993)’s methodology to robustify the original RS tests. The robust tests that require only ordinary least squares (OLS) estimation are able to identify the specific source(s) of departure(s) from the baseline linear regression model. An extensive Monte Carlo study provides evidence that our suggested tests possess excellent finite sample properties, both in terms of size and power. Our empirical illustrations, with two real data sets, attest that the tests developed in this paper could be very useful in judging the suitability of the SDM for the spatial data in hand.