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In medicine, needles are frequently used to deliver treatments to subsurface targets or to take tissue samples from the inside of an organ. Current clinical practice is to insert needles under image guidance or haptic feedback, although that may involve reinsertions and adjustments since the needle and its interaction with the tissue during insertion cannot be completely controlled. (Automated) needle steering could in theory improve the accuracy with which a target is reached and thus reduce surgical traumata especially for minimally invasive procedures, e.g., brachytherapy or biopsy. Yet, flexible needles and needle-tissue interaction are both complex and expensive to model and can often be computed approximatively only. In this paper we propose to employ timed games to navigate flexible needles with a bevel tip to reach a fixed target in tissue. We use a simple non-holonomic model of needle-tissue interaction, which abstracts in particular from the various physical forces involved and appears to be simplistic compared to related models from medical robotics. Based on the model, we synthesize strategies from which we can derive sufficiently precise motion plans to steer the needle in soft tissue. However, applying those strategies in practice, one is faced with the problem of an unpredictable behavior of the needle at the initial insertion point. Our proposal is to implement a preprocessing step to initialize the model based on data from the real system, once the needle is inserted. Taking into account the actual needle tip angle and position, we generate strategies to reach the desired target. We have implemented the model in Uppaal Stratego and evaluated it on steering a flexible needle in gelatin phantoms; gelatin phantoms are commonly used in medical technology to simulate the behavior of soft tissue. The experiments show that strategies can be synthesized for both generated and measured needle motions with a maximum deviation of 1.84mm.