Vector fields and differential forms living on fibred manifolds and their prolongations, and adapted to their fibred structure, can serve as an effective tool for geometrical (coordinate free) expression of all concepts of modern calculus of variations. (Practical calculations in concrete examples are then, using the general coordinate free expressions, made in appropriately chosen coordinates.) Special types of vector fields on the basic fibred manifold are vector fields of the defined type of projectability (with respect to the projection pi). They can be naturally prolonged on higher order prolongations of the basic fibred space and they have the key meaning in the calculus of variations serving as so called variations of sections. There are also special types of differential forms adapted to the fibred structure of basic spaces—horizontal and contact forms, contact forms forming the differential ideal. Differential forms with especially chosen types of horizontality serve as Lagrangians and Euler-Lagrange forms leading directly to the variational integral and equations of motion of a mechanical system, respectively. Distributions generated by vector fields or alternatively by differential forms are defined. Poincaré lemma adapted to the fibred structure is formulated and proved. Illustrative examples and pictures are present as well.