For explanations to the experimental fact that unstable acetylene and methylacetylene radical anions (A(-) and MA(-)) were observed in the trans-bent forms, we carried out a theoretical study based on calculations and theoretical analysis. The calculations were performed using (DFT) B3LYP, MP2, QCISD, and MRSDCI methods in conjunction with large basis sets, including diffuse functions on no centers (Bn), on carbons (Bn+), and on both carbons and hydrogens (B++). The trans-bent A(-) was located in the optimization calculations with all the basis sets used. It is characterized as a minimum-energy structure and is predicted to be more stable than the cis-bent form, and the isotropic proton hyperfine coupling constant (a(H)) values calculated on the trans-bent A(-) are in agreement with experiment. All these results confirm that A(-) exists in the trans-bent form.. The trans-bent form of MA(-) was located only at some of the levels of the calculations with the Bn and Bn+ basis sets. For the trans-bent MA(-), the B3LYP and QCISD calculations with the Bn basis sets predict a(H) values in agreement with those of the experiment. In the optimization calculations using the Bn++ basis sets, we got linear structures of MA(-) instead of the bent ones. Using Guerra's 6-311++G(d,p) basis, which contains moderate diffuse functions, we located the trans-bent MA(-), but the a(H) results were not good. Theoretical analysis invokes the Renner-Teller theory. The trans-bending potential energy curves Of the Ag-2 and (2)Bg states of A(-) were calculated. The two curves converge to the (2)IIg state of linear A(-) when the bending angle goes to 180 degrees, which describes the Renner-Teller splitting of the (2)IIg state of linear A(-) along the trans-bending coordinate. There exists a local minimum at a (trans) bending angle not equal 180 degrees along the curve of the lower state 2Ag, and the existence of the trans-bent A(-) is considered as a consequence of the Renner-Teller effect.