Four-dimensional spherical model of emotions was built with metric multidimensional scaling method. This model simultaneously describes emotional expressions in the oral human speech (based on the samples of the word “Yes”, spoken with different expressions) and vocalizations of rhesus macaque monkeys in the human listener’s perception. Based on statistical criteria, number of dimensions in the space of the perception of emotional human speech and monkey vocalizations samples was defined to be equal to 4. Stimuli points in the space are positioned in almost equal distance from the center of the hypersphere. Model space axes were interpreted in regard to the contents of human emotions. Orientation of perception of monkey vocalization samples space axes was conducted in a formal procedure based on direct experimental data — cross-assessment of the differences between some human speech samples and all monkey vocalizations samples. As a result, all studied monkey vocalizations samples were quantitatively presented in a unified system of the characteristics, defined for human emotions, and received an anthropomorphic interpretation. Obtained results are not controversial to the data from animal behavior observation and expert analysis of their vocalizations range. We revealed the similarity between emotional expressions in human speech and monkey vocalization range, which, in turn, demonstrates the relation of human and monkey emotions.