We present new numerical algorithms for solving the structural inverse gravimetry problem for the case of multiple surfaces. The inverse problem of finding the multiple surfaces that divide the constant density layers is an ill-posed one described by a nonlinear integral equation of the first kind. To solve it, it is necessary to apply the regularization ideas. The new regularized variants of the gradient type methods with the weighting factors are constructed, namely, the steepest descent and conjugate gradient method. We suggest the empirical rule for choosing the regularization parameters. On the basis of the constructed methods, we elaborate the parallel algorithms and implement them in the multicore CPU using the OpenMP technology. A set of experiments with the disturbed data is performed to test the gradient algorithms and study performance of the developed code. For the test problems with quasi-real data, these new regularized algorithms increase the accuracy and speed up computation in comparison with the unregularized ones. By using the 8-core CPU, we achieve the speedup of 8 times.