Constitutively secreted by endothelial cells, soluble FLT1 (sFLT1 or sVEGFR1) binds and sequesters extracellular vascular endothelial growth factors (VEGF), thereby reducing VEGF binding to VEGF receptor tyrosine kinases and their downstream signaling. In doing so, sFLT1 plays an important role in vascular development and in the patterning of new blood vessels in angiogenesis. Here, we develop multiple mechanistic models of sFLT1 secretion and identify a minimal mechanistic model that recapitulates key qualitative and quantitative features of temporal experimental datasets of sFLT1 secretion from multiple studies. We show that the experimental data on sFLT1 secretion is best represented by a delay differential equation (DDE) system including a maturation term, reflecting the time required between synthesis and secretion. Using optimization to identify appropriate values for the key mechanistic parameters in the model, we show that two model parameters (extracellular degradation rate constant and maturation time) are very strongly constrained by the experimental data, and that the remaining parameters are related by two strongly constrained constants. Thus, only one degree of freedom remains, and measurements of the intracellular levels of sFLT1 would fix the remaining parameters. Comparison between simulation predictions and additional experimental data of the outcomes of chemical inhibitors and genetic perturbations suggest that intermediate values of the secretion rate constant best match the simulation with experiments, which would completely constrain the model. However, some of the inhibitors tested produce results that cannot be reproduced by the model simulations, suggesting that additional mechanisms not included here are required to explain those inhibitors. Overall, the model reproduces most available experimental data and suggests targets for further quantitative investigation of the sFLT1 system.