Soft cosmic ray tomography has been shown to successfully discriminate materials with various density levels due to their ability to deeply penetrate matter, allowing sensitivity to atomic number, radiation length and density. Because the multiple muon scattering signal from high Z-materials is very strong, the technology is well suited to the detection of the illicit transportation of special and radiololgical nuclear materials. In addition, a recent detection technique based on measuring the lower energy particles that do not traverse the material (range radiography), allows to discriminate low and medium Z-materials. We have demonstrated it first using Monte Carlo simulations. More recently, using a Mini-Muon Tracker developed at Los Alamos National Laboratory, we performed various experiments to try out the radiation length technology. This paper presents the results from real experiments and evaluates the likelihood that soft cosmic ray tomography may be applied to detect high-explosives.