Gelatin is a popular material for the creation of tissue phantoms due to its ease-of-use, safety, low relative cost, and its amenability to tuning physical properties through the use of additives. One difficulty that arises when using gelatin, especially in low concentrations, is the brittleness of the material. In this paper, we show that small additions of another common biological polymer, sodium alginate, significantly increase the toughness of gelatin without changing the Young's modulus or other low-strain stress relaxation properties of the material. Samples were characterized using ramp-hold stress relaxation tests. The experimental data from these tests were then fit to the Generalized Maxwell (GM) model, as well as two models based on a fractional calculus approach: the Kelvin-Voigt Fractional Derivative (KVFD) and Fractional Maxwell (FM) models. We found that for our samples, the fractional models provided better fits with fewer parameters, and at strains within the linear elastic region, the linear viscoelastic parameters of the alginate/gelatin and pure gelatin samples were essentially indistinguishable. When the same ramp-hold stress relaxation experiments were run at high strains outside of the linear elastic region, we observed a shift in stress relaxation to shorter time scales with increasing sodium alginate addition, which may be associated with an increase in fluidity within the gelatin matrix. This leads us to believe that sodium alginate acts to enhance the viscosity within the fluidic region of the gelatin matrix, providing additional energy dissipation without raising the modulus of the material. These results are applicable to anyone desiring independent control of the Young's modulus and toughness in preparing tissue phantoms, and suggest that sodium alginate should be added to low-modulus gelatin for use in biological and medical testing applications.