This paper theoretically studies the mechanical behavior of buckling restrained steel plate shear walls (BRSPSW) with two-side connections and various height-to-width ratios. A concept of boundary restraining region at the edges of steel plates is proposed. Due to the restraining from the boundary restraining region, the middle portion of the steel plate is in pure shearing which is equivalent to the BRSPSW with four-side connections. The stress development in the BRSPSW with two-side connections is studied and a simplified formula is deduced to determine its load-bearing capacity. The results show that the steel plate with a small height-to-width ratio (<1.5) has a middle shearing region and boundary restraining regions at the left and right edges with a width of 1/3 of the height of steel plate. No middle shearing region occurs in BRSPSW with large height-to-width ratios (⩾1.5). It is found that the yielding region in BRSPSW with small height-to-width ratios is in an I shape and has a flange height of 1/10 of the height of the steel plate. For BRSPSW with small height-to-width ratios, the beam connected to the steel plate is subjected to shear forces at the middle imposed by the shearing region of the steel plate, and tensile or compressive force at ends by the boundary restraining region of the steel plate. For BRSPSW with large height-to-width ratios, only vertical tensile or compressive forces are transferred from the steel plate to the beam. The accuracy of the proposed formula for calculating the load-bearing capacity of BRSPSW is verified by comparing the numerical results, since the differences are within 10%.