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Abstract When the sinusoidal buckling of suspended tubular strings is transforming to helical buckling, the deformation changes drastically, which makes the tubular strings extremely unstable. The quantitative description of this buckling configuration in previous theoretical studies is not precise enough. In our current study, dynamic relaxation method is applied to carry out numerical simulation of buckling transition of suspended tubular strings. To obtain stable buckling configurations, larger Rayleigh damping is used to attenuate the dynamic effect. With the increase of axial compression load, the lateral buckling of the suspended strings suddenly becomes spiral shape with two contact points. As the string length increases, the position of the lower contact point remains almost at the same position. While the upper contact point gradually moves upward, and the helix angle between the two points increases and gradually tends to be constant. The maximum contact force is located at the lower contact point, the maximum shear force is located at the bottom of the strings, and the dimensionless distance between the location of the maximum bending moment and the well bottom is about 1.0. These loads, including the maximum contact force, maximum shear force and maximum bending moment, gradually decrease with the increasing string length and tend to be constant. The dimensionless critical load is reduced from 4.41 to 3.81 with the effect of string length. The critical load calculated in this paper is the minimum value when helical buckling just occurs. The results obtained in the current study have wide engineering applications, particularly in failure analysis and prevention of helical buckling. Highlights • Stable buckling configuration is obtained by using dynamic relaxation method. • Quantitative description of buckling deformation, shear force, bending moment and contact force are obtained. • The critical load obtained is the minimum one when the helical buckling just happens. [ABSTRACT FROM AUTHOR]