The method of generalized functions (GFM) has been developed to solve transientand vibrational boundary value problems of thermoelastic rod dynamics using a model of coupled thermoelasticity. Thermoelastic shock waves arising in such structures under the influence ofshock loads and heat flows are considered. Conditions on their fronts were obtained. Thesingularity of the assigned boundary tasks taking into account shock waves has been proved.On the basis of GFM, a system of algebraic resolving equations is built for a wide class ofboundary problems to determine their analytical solutions. Dynamics of the rod under the actionof forces and heat sources of various types, including those described by singular generalizedfunctions, which allow modeling the effect of pulsed concentrated sources, are studied. Computerimplementation of solutions of one edge problem at stationary oscillations was carried out, resultsof numerical experiments of calculation of rod thermodynamics at low and high frequenciesare presented. These solutions and algorithms can be used for engineering calculations of rodstructures to evaluate their strength properties.