In this work, the maximum constant rate that can be supported with a probability epsiv f exceeding certain delay bound D t is evaluated. Following the works in (Wu, 2003), the procedure to derive this capacity with probabilistic delay constraint CD t,epsiv is described. A simple closed form analytical result is given for block fading channel and different adaptive rate policies. The extension to the general correlated Rayleigh fading is also provided based on a semi-analytical strategy and the previous result for independent samples. As expected, CD t,epsiv tends to the ergodic capacity for long allowed delays (D t rarr infin) and diminishes when the delay constraint is more strict. The expected delay violation probability is compared to simulations in order to validate our results.