The linear and quadratic log contrast model with mixtures on the strictly positive simplex, $$ x_{q-1} = {(x_1, cdots, x_q):sum x_, = 1 and delta leq frac{x_i}{x_j} leq frac{1}{delta} for all i,j},$$ are considered. Using the invariance arguments, symmetric D-optimal designs are investigated. The class of symmetric D-optimal designs for the linear log contrasts model is given. Any D-optimal design for the quadratic log contrast model is shown to metric D-optimal designs for q=3 and 4 cases are given.