Searching for and reassembling elements that used to form one whole is a very common issue faced by archaeologists. This is because preparing an interesting museum exhibition consists in the presentation of objects that have been put together, not a pile of messily disassembled puzzle pieces. The article presents the concept of using linguistic methods in the process of joining elements of a 2D jigsaw puzzle. The method developed in the first stage creates the edge description of an object by defined unit vectors of the same length but different directions, and assigns them a designation in the form of letters, which leads to the creation of abstract words in the form of a sequence of signs. In the second stage, words with a defined length of strings belonging to two different objects are compared. The authors have created a program that performs an exhaustive search until the pool of available elements is fully exhausted. The conducted numerical experiments indicate the correctness of the method and effectiveness in determining the places of joining elements. The developed method will be useful to automate the reassembly of 2D elements from archaeological excavations.