The paper's aim is to determinate all cubic vertex-transitive graphs on up to certain order which is given in advance. A graph is $G$-vertex-transitive graph, if subgroup $G$ of graph's group of automorphism acts transitively on its vertex-set. Based on the number of orbits of the vertex-stabiliser $G_v$ in its action on the neighbourhood $\Gamma(v)$ we separate cubic vertex-transitive graphs into three groups. The first group is the group of graphs with only one orbit. Theorem, stating that the action of vertex-stabiliser on the neighbourhood has the same number of orbits as the action of group $G$ on arc-set, connects first group's graphs with cubic arc-transitive ones. The second group is the group of graphs with three orbits. Sabidussi's theorem connets second group's graphs with Cayley's graphs. The last group is the group of graphs with two orbits. Graphs from this group are connected with tetravalent arc-transitive graphs.
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