Accurate and reliable segmentation of catheters in MR-guided interventions remains a challenge, and a step of critical importance in clinical workflows. In this work, under reasonable assumptions, mechanical model based heuristics guide the segmentation process allows correct catheter identification rates greater than 98% (error 2.88 mm), and reduction in outliers to one-fourth compared to the state of the art. Given distal tips, searching towards the proximal ends of the catheters is guided by mechanical models that are estimated on a per-catheter basis. Their bending characteristics are used to constrain the image feature based candidate points. The final catheter trajectories are hybrid sequences of individual points, each derived from model and image features. We evaluate the method on a database of 10 patient MRI scans including 101 manually segmented catheters. The mean errors were 1.40 mm and the median errors were 1.05 mm. The number of outliers deviating more than 2 mm from the gold standard is 7, and the number of outliers deviating more than 3 mm from the gold standard is just 2.