Solar panels, can provide a useful and easy solution, to the thermal requirements of a building, such as home water heating. In addition to heating applications, there is also a need, to satisfy the increasing energy consumption, due to air conditioning during the summer months. Collectors fulfill this need, taking advantage of the green energy of solar radiation.The main focus of this thesis, is the mathematical and computational modeling and simulation of a flat plate solar collector, for the purpose of parametric analysis as well as risk analysis of uncertain weather variables.Starting with Chapter 1, the two categories of solar collectors, are introduced (concentrated and non-concentrated solar collectors). The five categories of concentrated solar collectors are listed with a brief description of them, and then a more extensive reference is made to the two types of non-concentrated solar collectors, the flat plate collectors and the vacuum collectors. Finally, the different types of models are listed, illustrating the utility of each modeling.In Chapter 2, the mathematical modeling of the solar collector is presented. More specifically, the mathematical equations and procedures of finding, the coefficient of total heat loss, the factors of efficiency, heat gain and flow, as well as the efficiency of the collector are analyzed here.Chapter 3, presents and explains the computational code, programmed in the program Matlab. The program code, accepts data as input (collector characteristics and weather variables) and returns, the results mentioned in the previous chapter, most importantly the efficiency of the collector. In addition, to this chapter, the validation of the program is checked. In order to verify that the program is working properly, valid source data and results are used, where the data is entered into the thesis program and the returned results, are compared with the results from the source.The penultimate Chapter 4, focuses on collector parameter optimization. Initially diagrams of behavior, of the parameters we are interested in, regarding the degree of performance are presented. A regression analysis, is then carried out, in order to give a numerical order, of the parameters causing change in the efficiency. At the end of the chapter, risk analysis is performed, on uncertain weather variables, using the Monte Carlo method. This is achieved, by introducing random variable generators, that follow distributions related to each variable, and repeating the code multiple times. The results are collected, examined and grouped into clusters, then their average value, distribution and probability of each cluster, are calculated. Finally, a diagram is presented, to determine the convergence of the value according to the number of code repeats.In conclusion in Chapter 5, are summarized the most important observations and conclusions drawn from the results presented in the sections above.