Abstract: A new algorithm to study the fundamental point in solid test for free-form solids is presented. The test is performed efficiently and robustly because it does not use trigonometric functions and it makes it unnecessary to deal with complex special cases. The algorithm is based on considering the solid as composed of original tetrahedra and free-form cells, and it computes the test in two stages: evaluation of the point inclusion in these simple elements and merging of the results in a simple sum. The solid boundary is defined as a set of low-degree triangular Bézier patches.