The disclosure relates to a mine shaft conveyance safety brake for controlling the rate of deceleration of a free-falling conveyance, operating within or upon fixed shaft guides, in a vertical, substantially vertical or inclined mine shaft. The safety brake includes an activation system, one or more guide clamp assemblies operable for locking onto one or more shaft guides, one or more braking assemblies and one or more brake paths attached upon the conveyance. Upon detection of a conveyance suspension failure or slack rope condition associated with a free-falling or obstructed condition of the conveyance, the activation system is triggered, causing each guide clamp assembly to self-lock onto a shaft guide. Upon further downward travel of the conveyance, the braking assemblies travel upwardly upon the brake paths, generating increasing braking forces in a controlled manner until the conveyance comes to a controlled stop. The safety brake is purely mechanical in nature, as there are no electronics, electro-mechanical controls or hydraulic systems involved.