The paper evaluates whether the Lusaka Stock Exchange (LuSE) is weak form efficient, and whether stock price movements conform to the random walk hypothesis of non-predictability in future price movements based on past price information. The methods employed are the parametric and non-parametric individual as well as multiple variance ratio tests. In addition, the study incorporates the Runs Test. The study further examines seasonality in Zambian stock returns of the day of the week effect as well as monthly related effects. The period of analysis is from 3rd January, 2006 to 17th February, 2014. The study incorporates daily data as well as monthly data of the LuSE All share Index in order to investigate the random walk hypothesis as well as seasonality effects of the Zambian market. The period of analysis is broken down into two sub periods after accounting for multiple structural breaks in the data. The results of the study are mixed, the results of the Runs test finds the Zambian stock market price series to be mutually independent and conform to a random sequence, and are as such unpredictable. While the variance ratio tests reject the random walk hypothesis for the Zambian market, and as such, support the view of the use of technical trading strategies in order to outperform buy-and-hold strategies. The study finds no evidence of any seasonality in the data, either for daily data as well as monthly data. As such there is evidence that investors may acquire returns greater than those of the market, however, transaction costs and commissions would have to be minimal in order to exploit any patterns in the stock price series of the Lusaka stock exchange.