Effectively solving the governing equations for contact problems often involves complex mathematical theory, while the distribution of contact stress is highly random in practical engineering applications. This study proposes a novel algorithm based on the triangular load discrete element and the discrete convolution fast Fourier transform (DC-FFT) algorithm. This algorithm provides a high-precision and reliable method for efficiently solving the contact response of a solid under any load distribution. Compared to the commonly used uniform load element discrete method, the analytical solution of the triangular element is more complex. However, it better simulates the characteristics of contact load distribution, accounting for situations where the load at the contact edge increases from zero or decreases to zero. The stress component under the action of the triangular and uniform load elements is derived based on the “excitation-response” characteristics of the contact influence coefficient matrix. This information is used to optimize the solution method of the triangular load discrete element. By constructing the stress solution in the form of a discrete convolution, including the influence coefficient matrix, the stress superposition effect of a target node under the action of all elements can be further simplified and accelerated by using the DC-FFT algorithm for highly repetitive matrix calculations. Programming and calculation analysis show that the proposed algorithm based on the triangular load element is accurate and efficient.