Slope is a typical disaster in open-pit mining. Then it is a kind of non-continuous and uncertain natural geological body. In this case, common assessment approaches cannot assess the slope stability problems with both certain and uncertain information. Then, a neutrosophic number (NN) can easily represent the certain and uncertain information. Unfortunately NNs have not been applied in slope stability analysis so far. Therefore, this paper proposes the arctangent and tangent similarity measures of NNs and a slope stability assessment method using the arctangent and tangent similarity measures of NNs. By the similarity measure between the classification grades of slope stability and a slope sample with NNs, we can determine the as-sessment grade of the slope sample/case. Then, the assessment results of ten slope samples/cases demonstrate the same as ac-tual grades of the ten slope cases, which indicate the effectiveness and feasibility of the proposed slope stability assessment method. The advantages are that the slope stability assessment method based on the arctangent and tangent similarity measures of NNs is simple and suitable and can assess slope stability problems in NN setting.