PurposeIn the article, analytical model of first-order shear deformation (FSDT) beams made of jute–epoxy is presented to study the low-velocity impact response.Design/methodology/approachThe nonlinear Hertz contact law is applied to identify the contact between projectile and beam. The energy method, Lagrange's equations and Ritz method are applied to derive the nonlinear governing equation of the beam and impactor-associated boundary condition. The motion equations are then solved simultaneously by the Runge–Kutta fourth-order method.FindingsAlso, a comparison is performed to validate the model predictions. The contact force and beam indentation histories of the jute–epoxy simply supported beam under spherical impactor with different radius and initial velocity are investigated in detail. It is found that in response to impactor radius increase, the utilization of the contact force law has resulted in a same increasing trend of peak contact force, impact duration and beam indentation, while in response to impactor initial velocity increase, the maximum contact force and beam indentation increase while impact time has vice versa trend.Originality/valueThis paper fulfills an identified need to study how jute–epoxy beam behavior with simply supported boundary conditions under low-velocity impact can be enabled.