Exercises for muscles of biceps and triceps are among the most popular exercises in fitness centers. Due to a lack of research on the topic from engineering point of view and due to a wide popularity of upper arm exercises, there is a need for biomechanical analysis of exercises for biceps and triceps. Biomechanical analysis on free weight exercises was based on establishing the differences between correct and incorrect movements which can lead to injuries or decrease muscle activation, which decreases efficiency of exercises. Biomechanical analysis was applied for three exercises which activate biceps and for four exercises which activate triceps. It can be concluded from biomechanical analysis that the biggest advantages of free weight exercises are freedom of movement and activation of stabilizing muscles. It is also possible to detect muscle disbalance if it exists. Furthermore, market overview of the most common machines available in regular fitness centers has been shown as well as their pros and cons in regard to exercises with free weights. Finally, drafts of suggestions are given for improving machines which are based on improving the ergonomics of machines and efficiency of machine exercises, which would improve their popularity in fitness centers. Suggestions which improve machine ergonomics are adjustable angle for handles and adjustable incline for armrest which also enables the machine to “hit” different parts of muscles. The first suggestion which improves machine efficiency is the possibility of supination in the machine exercise. In this way the movement would include the second function of biceps. The second suggestion is implementation of different types of handles so that a user could simulate more types of free weight exercises. Last but not least, the target group in this paper were people with disabilities to whom upper arm muscles are extremely important. Suggestion drafts are given in order to adjust the machines for them. They include the possibility to remove a seat so that the user could be placed in the right position in his wheelchair, the adjustment of armrest height (because it is not possible to adjust the height of a wheelchair) and placing weights on a platform of certain height so that the user could change load as easily as possible.