Optimum conditions in muon catalyzed fusion is very important for increasing the number of fusion. Usually the medium is considered liquid mixture, gas or solid layers. Using solid HT layer with very low concentration of tritium has been suggested for producing a µt atom beam. In this thesis, this suggestion is investigated at first. Then the optimum conditions are determined for solid, liquid and gaseous HT targets. The Ramsauer-Townsend effect and transfer of muon from µp to µt atoms are very important parameters for this investigation. In other words, by entering muon to a solid HT layers or liquid, we can use it as µt generator. This designing for production of µt atoms can be used in the measurement of dtµ molecule formation rate. In addition, it can be used to designing of solid layers or liquid of hydrogen isotopes for muon catalyzed fusion. We have shown that the flux of µt atoms in HT layer is maximum at C t =0.01. In this condition the transfer of muon from µp atoms to µt atoms is about 90%. Then, considering various layer arrangements including 3-layer of HT/D 2 /DT, 2-layer of HT/DT and 1-layer of DT arrangement for solid and liquid mixtures, the optimum concentrations of tritium in first layer and fusion layer for maximum fusion of muon catalyzed fusion are determined through the solution of the layers kinetic equations via the fourth orther Range-Kutta method by the Matlab software. There are equations for fusion cycle in solid environment proposed by others that it seems to have some miscues and must be corrected. After the solution of the corrected equations, the computational results are compared with the previous results. We have shown that in contrast the previous works, using the 3-layer decreases the fusion yield, however it is increased in solid compare with liquid targets. Finally, a multilayer arrangement in the spherical HT and D 2 layers is proposed for increase of the fusion yield and its conditions are studied. Keywords: Muon catalyzed fusion, Ramsauer-Townsend effect, µt atomics source, liquid and solid multilayer of HT, D 2 , DT.