The statistical, associating fluid theory for potentials of variable range (SAFT-VR) is used to predict the fluid phase behavior of elastin-like polypeptide (ELP) sequences in aqueous solution with special focus on the loci of lower critical solution temperatures (LCSTs). A SAFT-VR model for these solutions is developed following a coarse-graining approach combining information from atomistic simulations and from previous SAFT models for previously reported relevant systems. Constant-pressure temperature composition phase diagrams are determined for solutions of (VPGVG)(n) sequences + water with n = 1 to 300. The SAFT-VR equation of state lends itself to the straightforward calculation of phase bmindaries so that complete fluid-phase equilibria can be calculated efficiently. A broad range of thermodynamic conditions of temperature and pressure ate considered, and regions of vapor liquid and liquid liquid coexistence, including LCSTs, are found. The Calculated phase boundaries at low concentrations match those measured experimentally: The tempetaturecomposition phase diagrams of the aqueous ELP solutions at low pressure (0.1 MPa) are similar to those of types V and VI phase behavior in the classification of Scott and van Konynenburg. An analysis of the high-pressure phase behavior confirms, however, that a clbsed loop liquid liquid" immiscibility region, Separate from the gas liquid envelope, is present for aqueous solutions of (VPGVG)30; such a phase diagram is typical of type VI phase behavior. ELPs with shorter lengths exhibit both liquid liquid and gas liquid regions, both of which become less extensive as:the chain length of the ELP is decreased. The strength of the hydrogen-bonding interaction is also found to affect the phase diagram of the (VPGVG)30 system in that the liquid liquid and gas liquid' regions expand as "the hydrogen-bonding strength is decreased and shrink as it is increased. The LCSTs of the mixtures are seen to decrease as the ELP chain length is increased.