In this thesis we will be dealing with plasticity in metric spaces. Plastic metric spaces can be In the article «Dehnungen, Verkürzungen, Isometrien» written by H. Freudenthal and W. Hurewicz, non-contractive, non-expansive and isometry functions are defined. Also in this article, we can see that a surjection mapping of a totally bounded space onto itself is either an isometry or there will be a pair of points whose distance increases under this mapping and another pair of points whose distance decreases. We will use this as motivation for the thesis. But on the other hand, it goes beyond this subject in that the decreasing of the distance between a pair of points implies the increasing of the distance between another pair of points. Also in the article «Pog?ebione studium hipopotama» by W. Nitka, the author defines CE-spaces. In this article we see that CE-spaces were first called by B. Knaster «hippopotamus spaces» . Apparently they were given this name because some employees at the local zoo had remarked that the skin of a hippopotamus is so tight that when it contracts in one area, it expands in another. Many results was concluded about the EC-plastic spaces. For example it is proved that every totally bounded space is an EC-space. Also, every discrete metric space with the 0-1 metric is an EC-plastic space because every bijection is an isometry. On the other hand, by means of examples one can show that EC-spaces need not be locally compact, compact, complete, or bounded. In this thesis, we focus on the EC-plastic spaces and of course NEC-plastic spaces are also covered, because the motivation in this thesis is related to the EC-spaces. In this thesis, other topics such as «plasticity properties of the sets» and «hereditarily EC-plastic spaces» are also investigated. «Plasticity properties of the sets» deals with different sets and consider plasticity properties for them. First, we can see that the integers metric space is an EC-space. While so far every example of an EC-space we have given has been bounded. Then we see various examples of types of plastic spaces. After that, most discussions about products of EC-spaces and the completion of an NEC-space. Also, in «hereditarily EC-plastic spaces» we are looking for properties that assuming them, an EC-space will be hereditary. It should be noted that no metric space can be a hereditarily NEC-plastic space, because every finite suace of an NEC-space is an EC-space. But hereditarily EC-spaces do exist. In fact any totally bounded metric space has this property. In the end, we are looking for simple characterization of EC-spaces and also CE-spaces, this will be mentioned formally as an open problem.