Vast number of researches deliberated the separation of speech mixtures due to the importance of this field of research . Whereas its applications became widely used in our daily life; such as mobile conversation, video conferences, and other distant communications. These sorts of applications may suffer from what is well known the cocktail party problem. Independent component analysis (ICA) has been extensively used to overcome this problem and many ICA algorithms based on different techniques have been developed in this context. Still coming up with some suitable algorithms to separate speech mixed signals into their original ones is of great importance. Hence, this paper utilizes thirty ICA algorithms for estimating the original speech signals from mixed ones, the estimation process is carried out with the purpose of testing the robustness of the algorithms once against a different number of mixed signals and another against different lengths of mixed signals. Three criteria namely Spearman correlation coefficient, signal to interference ratio, and computational demand have been used for comparing the obtained results. The results of the comparison were sufficient to signify some algorithms which are appropriate for the separation of speech mixtures.