DNA transposons are mobile genetic elements made of a gene coding for the enzyme transposase flanked by terminal inverted repeats. Transposase binds terminal inverted repeats and catalyzes transposition of the transposase gene which enables DNA transposons to mobilize. Based on the transposition mechanism employed by DNA transposons, synthetic transposon systems, that utilize a plasmid with region of intereset flanked by terminal inverted repeats and in trans expression of the transposase, were developed. These systems ensure stable genomic integration of an expression cassete into genomes of animal cells and are an alternative to viral and non-viral methods for gene transfer. In order to have long lasting expression of transgenes insulator sequences are added to vectors. Insulators are regulatory DNA sequences that make chromatin barriers which protect genes from silencing. The aim of this thesis was the construction of vector system based on transposon technology that will ensure stable integration and long-lasting expression of transgene in the host genome. Two plasmid vector systems based on sleeping beauty (SB) and piggyBac (PB) DNA transposons respectively were successfully constructed. Two SB inverted terminal repeats and two PB inverted terminal repeats were cloned into both plasmids repectively with addition of four insulator sequences in each plasmid using restriction and ligation methods. Same methods were used to construct an expression vector that will express PB transposase in trans. Validity of all plasmid construct was confirmed using restriction analysis or colony PCR and sequencing.