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This paper presents an investigation into the tensile strength, modulus of elasticity, Poisson’s ratio, and stress–strain relationships of alkali-activated portland-cement-free concrete made with fly ash or ground granulated blast furnace slag (GGBFS) as the sole binder. Alkali-activated concrete is shown to be stronger in tension and have lower Poisson’s ratio than portland cement concrete. Relationships are proposed to estimate the tensile strength and modulus of elasticity based on the compressive strength of alkali-activated concrete, which are of the same form as those currently employed for portland cement concrete.