Ice and snow structure is a novel type of structure, which attracts more and more attention. As a novel green building material, the research of plain ice and fiber-reinforced ice material is the basis of ice and snow structures. This study aims to investigate the tensile mechanical properties and stress–strain constitutive relationship of plain ice and pulp fiber-reinforced ice (PFRI) by direct tensile tests. The experimental variables studied included the fiber contents (0%, 1%, 2%, 4% and 6%) and temperatures (-20 °C, −15 °C, −10 °C and −5°C). The results showed that the plain ice was more brittle under tension, while the PFRI material had the failure progress of crack generation, crack propagation and fracture, showing quasi-brittle characteristics. The peak strength, peak tensile strain and elastic modulus increased with the decreasing temperature. With the increase of fiber content, the peak strength and peak strain increased, while the elastic modulus decreased. Based on the experimental results, the prediction models of peak strength, peak strain and elastic modulus with respect to temperature and fiber content were established. As for plain ice, due to the strong brittleness, the direct tensile strength was basically the same as the splitting tensile strength. The direct tensile strength of PFRI was about 1.28 times the splitting tensile strength, and the direct tensile strength can better reflect the tensile properties. A segmented empirical constitutive model based on experiments and a damage constitutive model based on continuous damage theory were established. The damage constitutive model was embedded in ABAQUS by user defined material subroutine (UMAT) for finite element analysis, and the energy regularization of crack bond model was used to ensure the mesh size independence of the results. It showed that the proposed constitutive models can effectively predict the stress–strain behavior and failure characteristics of ice materials. This study will provide an important basis for the design and construction of ice and snow structures.