This paper examines bubbles on the JSE All Share Index as well as the critical time of the stock market crash from 2/01/ 2004 – 27/03/2014. The underlying hypothesis define bubbles as extreme and begin as a group of small events which grow in a super exponential form explained by a log periodic power law model (LPPL model). The hypothesis is based on the assumption of investors’ herding behavior, where investors collude by making investment decision correlated with their counterparties. The paper implements a Savitzky Golary Algorithm to detect peaks and calculate the critical time of the crash from the peaks. An Ordinary Least Squares (OLS) method is used to determine both the value of stock market price index at the critical time and the increase in the stock market price index over the time before the crash. The remaining parameters of the LPPL model are estimated using a Maximum Likelihood Estimation method. On the empirical results; 68 peaks were detected, and the LPPL model at the critical crash time is estimated 34736.586. Five bubbles are detected; the 15/8/2005 bubble, 28/5/2013 bubble, 23/8/2013 bubble, 5/11/2013, and 1/20/2014.