In this work, a new graphical and mathematical model is presented as a new approach for Deterministic Timed Arc Petri Net. In the proposed Timed Arc Petri Net, time is associated with arcs in transition firing process. In the graphical model, a new triangular graphical element, namely time element is used. The time element allows the user to observe the whole firing process graphically via observing temporarily invisible tokens, which can become temporarily invisible and re-visible in Timed Petri Nets during the firing process of transition. In the mathematical model, firing processes are realized by unit impulses and the resulting states are represented by the marking vector, which represents the number of tokens in all places; the time element vector, which represents the number of flowing tokens in time elements; the remaining time vector, which represents the time-status of these flowing tokens.