He was awarded in 1982 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category. Apart from this, he won various other prestigious awards some of them are FICCI Award, which is Highest National Award by Industry in Physical Sciences including Mathematics, Awarded by Federation of Indian Chamber of Commerce and Industry (FICCI) in 1980 and Distinguished Service Award in Mathematical Sciences from Vijnana Parishad of India in 1997.Prof. Shukla had proposed a new deterministic theory regarding the effect of surface roughness in lubrication. He has done significant work on biofluid dynamics, in particular peristaltic transport of faeces in intestines and on interaction of biorheological aspects of blood flow and arterial stenosis. He has also made contributions in the area of population dynamics of interacting species and mathematical theory of epidemics by taking into account environmental effects.