Abstract <p>For a multivariate polynomial regression model, the problem of constructing a <i>D</i>-optimal design on a symmetric (relative to the origin) design region is studied. Based on the symmetry property, an approach, which reduces the computational complexity of constructing the optimal design, is proposed. For the case of an asymmetric region, an algorithm for constructing <i>D</i>-optimal designs for a multivariate quadratic polynomial model without a constant term is developed. This model has significant practical importance and can be used in various applications, such as calculating the service life of road surfaces depending on a variety of factors.</p>