Proppant is sometimes produced along with hydrocarbons in hydraulically fractured petroleum wells. Sometimes 10% to 20% of the proppant is backproduced, which can lead to damaged equipment and downtime. Furthermore, proppant flowback can lead to a substantial loss of fracture conductivity. A numerical study was conducted to help understand what conditions are likely to lead to proppant flowback. In the simulations, the mechanical interaction of a large number (several thousand) individual proppant grains was modeled with a distinct-element-type code. The numerical simulations show that hydraulic fractures propped with cohesionless, unbonded proppant fail under closure stress at a critical ratio of mean grain diameter to fracture width. This is consistent with published laboratory studies. The simulations identify the mechanism (arch failure) that triggers the mechanical instability and also show that the primary way that drawdowns (less than approximate to 75 psi/ft) affect proppant flowback is to transport loose proppant grains in front of the stable arch to the wellbore. Drawdowns >75 psi/ft are sufficient to destabilize the arch and to cause progressive failure of the propped fractures.