The stock market has different cycles, such as, four-year presidential cycle, fiscal reporting cycles. In addition, some cycles are defined by intrinsic characteristic properties of the system. The stock market performance curve can be considered as a sum of the cyclical functions with different periods and amplitudes. It is not easy to analyze the repetition of typical patterns using a simple chart analysis because cycles mask themselves - sometimes they overlap to form an abnormal extremum or offset to form a flat period. Stock Market Analyzer-Predictor SMAP-3 is able to extract basic cycles of the stock market (indexes, sectors, or well-traded shares) and to predict an optimal timing to buy or sell stocks. Its calculation mainly based on extracting basic cyclical functions with different periods, amplitudes, and phases from historical quote curve. To detect correctly major cycles, the historical price data are transformed from time domain to frequency domain (spectrum). At the beginning SMAP-3 does a simulation (back testing) of forecast on relevant past data in order to estimate the accuracy of prediction with certain parameters. Then it calculates the prediction for the time period forward using internal optimized parameters. Using back testing also allows user to find an optimal time frame. By selecting data with different historical periods, user can identify the major cycles, which have a dominant effect in a particular time frame. To build an extrapolation (predicted curve), SMAP-3 uses the following two-step approach: (1) applying spectral (time series) analysis to decompose the curve into basic functions, (2) composing these functions beyond the historical data. SMAP-3 also enables finding optimal timing to buy/sell by analyzing month of year, day of month, and day of week (the calculation is based on statistical analysis). SMAP-3 has a user-friendly easy-to-use interface. This software is intended for investors with a basic knowledge in stock investing.