Many-Task Computing (MTC) is a common scenario for multiple parallel systems, such as cluster, grids, cloud and supercomputers, but it is not so popular in shared memory parallel processors. In this sense and given the spectacular growth in performance and in number of cores integrated in many-core architectures, the study of MTC on such architectures is becoming more and more relevant. In this paper, authors present what are those programming mechanisms to take advantages of such massively parallel features for the particular target of MTC. Also, the hardware features of the two dominant many-core platforms (NVIDIA GPUs and Intel Xeon Phi) are also analyzed for our specific framework. Given the important differences in terms of hardware and software in our two many-core platforms, we have considered different strategies based on CUDA (for GPUs) and OpenMP (for Intel Xeon Phi). We carried out several test cases based on an appropriate and widely studied problem for benchmarking as matrix multiplication. Essentially, this study consisted of comparing the time consumed for computing in parallel several tasks one by one (the whole computational resources are used just to compute one task at a time) with the time consumed for computing in parallel the same set of tasks simultaneously (the whole computational resources are used for computing the set of tasks at very same time). Finally, we compared both software-hardware scenarios to identify the most relevant computer features in each of our many-core architectures.