Upward lightning occurs generally from tall structures. The mechanism of the initiation of upward lightning is not yet fully understood. Upward lightning can be classified into two categories based on either the absence or the presence of other lightning activity prior to the upward flash. This work proposes an explanation of how upward lightning flashes can be triggered by nearby lightning activity. It is generally thought that the lightning activity prior to the flash will intensify the electric field at the tip of the tall structures. However, to the best of our knowledge, no attempt has been made to evaluate theoretically this hypothesis. In this paper, we derive analytically the electric field enhancement on the ground (or at the top of tall structures) based on different triggering scenarios. These fields are later used in a simplified corona model to evaluate if they are able to trigger upward lightning. It is shown that both slow processes such as leader propagation and faster return strokes can trigger an upward negative flash from relatively short structures of a few tens of meters, even without any slowly varying background electric field. This study confirms theoretically experimental observations and it provides new insights into the mechanisms of initiation of upward flashes from tall structures.